They'd want something that lets them flap their wings, and something that doesn't create drag or cause them to be blown off course.

That means tight fit clothes are your only option. Loose fit like a poncho would cause all sorts of trouble when flying.

The only issue is how to put on a tight fitting jacket with those oversized wing-arms? Consider the folowing life-jacket first:

You can put this on by throwing the back flap over your head, pushing your head through the hole and then afterwards pull the strap around your waist. No matter how big your wings are, they'll fit through those side holes without problems.

To get a tighter fit with fewer open holes on the sides the straps can be replaced with a zipper below each arm-wing.

The only difference with the image above is that the zipper ends below the arm-wing hole the same way our own jacket zippers end below our chin.

If they are like bird, having feathers on their body, they don't need clothes for covering, since feathers provide an excellent insulation. Moreover, covering the feathers will have a detrimental effect on the flight ability.

If they instead are like bats, they have to wear something tight fitting, in order to not disturb the aerodynamics of their wings. It also has to be really lightweight, to not add excessive burden and prevent their flight.

As you probably have already noticed, lightweight, thermal insulating and elastic leads to technical fibers, which we have developed in the very recent past. That would mean that, with a tech development similar to our, your flying-people would have been naked for most of their history.

In both cases it would be preferred to wear something like a gilet, leaving the wings free and uncovered, again for not disturbing their aerodynamic properties.

If they are like humanoid people --- head, torso, two arms, two wings, two legs --- and whether they can fly or not, they might wear a variety of clothing, depending on circumstance.

At home, being comfortable and with nowhere in particular to go, winged folk frequently opt to wear nothing at all. There's no good reason to get all dressed up when you're just going to lounge around in a hammock anyway!

For travelling by foot or working around their village, various jobs would require clothing of some kind. Woodworking, gardening, hunting, stone cutting. They'll want to wear some kind of apron to protect their bits (especially if they're guys); and also some kind of sarong or britches and perhaps sandals or boots. A belt or two with an assortment of kit bags, knives and tools would round out the ensemble.

Winged people, though often erroneously so portrayed, rarely wear any kind of upper body clothing. Shirts, vests, jackets, frock coats: all of these articles of clothing are unwearable by winged folk. No indeed! As any winged person can tell you, trying to stuff one's wings through a tiny hole in a shirt would be a losing battle!

Winged folk do, however, like to decorate themselves, and so will often wear a colourful sarong and may decorate their bodies and faces with various kinds of pigments. Some decorative upper body garments include scarves, abdominal wraps and shawls. Colourful and patterned, of course!

As for flying, for example in an airship, winged folk prefer knickers with pockets, leggings, a flight cap, goggles and sometimes a bandanna worn around the face. Bugs, you know.

For those winged folk who can fly by their own power, they too prefer a kind of britches, but tighter fitting, along the lines of jodhpurs, which won't flap about too noisily but also offer protection.

I think this is too complex to be specific.

Weather and climate and cultural norms all come into what is appropriate/acceptable/practical to wear. A police flying person in winter is going to wear something totally different from a flying person at the beach in summer. I have summer jackets and winter jackets. I have a rain jackets that rolls up and stows away in a small pouch. What I don't have is one outfit type that does everything and can (or should) be used everywhere. When I was young ("a short time ago" :-) ) my women would be loath to leave the house without a scarf on their heads - it was the norm (and nothing to do with what men wanted either). Fashion and cultural norms dictate a lot of what we wear. Men and women continue to wear idiotically impractical things (even uncomfortable thing) that are part of a cultural norm they adhere to (e.g. high heels - I smart women wearing high heels which are just physically way off what is good to wear).

Flying creates different issues : it's probably more like running than normal locomotion (not how much time birds spend standing, sitting and walking in practice). What do people wear when they do sports ? They were sport specific outfits (and a wide variety).

How high do they fly ? High flying is different from near ground stuff - ask anyone who flies a small aircraft. Note that being in a e.g. thirty mile an hour wind because you're flying through air is quite different from how you'll feel standing still or walking.

They might not want to flap their wings - e.g. business presentation to CEO does not seem appropriate to flap wings. Most of they day could be spent not flapping or using wings. Do you spend most of your day running or jumping - most people don't do those things most of the time - even if they do manual labour. Maybe your flying creatures commute to work on the bus because it's less exhausting, takes less time and doesn't turn them into sweaty mess - that's why we don't typically run to work.

Maybe wings would have bra-like support garments designed to keep them comfortably out of the way most of the time (which is at least one supposed function of a bra). In one culture you might be expected to hide your wings normally and in another they're on display.

And the physical design of the creature is also rather significant. Exactly where are the wings ? How big ? Covered in what ? Delicate ? Tough ? Sensitive ? Are their arms as well (birds don't have arms) ? There is likely a balance issue - walking with tightly bound wings might be very unnatural (or might not) ? The opposite might apply.

What about covering wings with e.g. looses sleeve that can be removed (like leggings or stockings) ?

There's just way too many variables for a single answer. You might say (I'm sorry, I have to do this) that the sky is the limit. :-)

Decades of research has already been put into this topic.

The results can be seen in this illustration from The Top 10 Comic Book Superheroes Who Can Fly:

(The skin-tight clothing makes sense, but I don't understand the purpose of the flapping capes though.)

You might be interested in Hawkman in particular.

Undergarments: I want to be properly supported while flying -- I would want a bra as supportive as a sports-bra, but it would need to clasp-on, like Hawkman's Harness.

I agree with @elimtilas on an Apron-style for shirt/dress, protecting the torso, and also allowing one to carry tools. (Pockets would all have ZIPPERS or other such fastenings.)

Pants/Skirts - can be any style, but probably on the tight side -- perhaps converts into something more flowing when on the ground.

Shoes -- if they kinda "float" whenever they want to maneuver on ground-level, then footwear may become purely decorative. But they could also be perhaps like a foot-helmet -- focused on minimizing impact with bad landings?

We don't only wear clothes to not be naked, the provide us protection from cold/heat, the sun, the wind, insects, dirt etc. (Since we lack fur, feathers). So pants and shirts would probably be a thing. One other thing that seems to go unnoticed, is that we wear shoes - we protect our transportation organs. Which makes me think that your people would definitely wear wing-protecting-flying-enhancing-ware. And as for the trouble to put on complicated clothes or not very comfortable, I'll leave these here: shoe laces, high heels, high boots,shirts with tens of buttons, dresses with zippers on the back, skinny jeans etc...

Like everyone else has pointed out, definitely not loose clothing.

But more importantly, if you're flying high, I think it would be sensible to consider conditions like temperature and pressure.

Temperature reduces as altitude increases. So, one might want to consider wearing clothing that adequately caters for temperatures lower than the current temperature (on the surface).

Pressure also reduces as altitude increases. This means the air would be thinner. You wouldn't want to wear something that would suffocate you.

If we are talking about humans as in after at least 20,000 years of unhealthy eating, fattening up, sitting on chairs and going for silly fashions, they'll wear power suits with propellers. Or at least something with improved aerodynamic properties, like we use shoes instead of growing half inch thick calluses on the soles of our feet.

Also, there will probably be the equivalent of bycicles or scooters, only powered by their very strong arms instead of their (comparatively) weak legs.

None.

If they are flying, it means they've already evolved to best flying adaptation. Clothes would only add weight and drag which would hinder flying. The difference between them and us is that while walking/running has lot's of extra capacity, flying is a cutting-edge activity that leaves no room for fooling around. Any clothes would drastically cut down range while increasing effort. For them a simple undershirt would be something like wearing a full plate armour for us.

If there were people with wings, who didn't want to be naked all the time

They wouldn't. As we evolved to want clothing in colder climates, they would evolve to want to be naked for best flying performance. Flying species would consider clothes as something as repulsive as we consider nudity.

If you say they have wings like a bird then they need help donning clothing as their delicate end feathers would snap with the effort. Otherwise I'll assume these feathers bend at the users will to become long soft fingers. If this is the case you can't cover the feather arms spans so you can use a vests with Velcro or areas or patches that when pressure is held for a moment will seal in place to keep the fabric together but then the issue is taking it off with that maybe using circular or side to side rub/swipe will change how the patches work to release the seal.

If you do the fairy style in the back near the shoulder blades model of wings then you want farm bib style the thin section at the spin splays over the shoulders to attach upfront so you're keeping the wing area closest to the skin clear. Now you can add more back fabric and add in cool linking designs because they now have humanoid fingers but you need that wing span and full range of motion to be priority as flying is a life or death action.

Carnaval Row is a great show to showoff how not to design everyday wear for winged humanoids their capes don't split apart at the back when they want to fly, how do their winds get fitted into the slits in the back of their humanoid clothing? Cuz it shouldn't the only thing in that show that worked for fairy kind were the weighted belts they put over the wings to stop them from flying away.

When designing clothing around appendages you need to think how will these wings work? You can don wings at home now how can you manage clothing to cover 99% of your skin and leave room for the joining section of wing and skin? With trial and error you'll figure it out its just if you have physical wing arms then you need a helper species to make and dress your people.

I believe the future of humanity is in the atmosphere and as this might be the case I'd argue that they would be wearing gases. particularly girls would wear pink clouds and dudes will wear blue or purple ones also with future advancements such as in the areas of nano-tech underwears could be some sorta hugging-nanites to provide a desirable body temperature during flight(Imagine the need not to wear a cardigan inorder to flyover cold skys of Winnipeg in canada no more but back then in that future).

gases are really light and if the technology is further developed the gas-clothe may even generate some additional lift if its in a way made to cling tightly to the wearer's skin and is indeed less denser than the surrounding air or say the gas fabric is some kinda ultra-maglev-air-molecules that gets repulsed by the atmosphere