Alter self can turn your body into anything as long as you basically retain the same body shape. It can even change your weight. Moreover, it can transform you into a member of another race.
So, this spell can, in theory, grant the caster flight in two ways:
- Turn yourself into an Aarakocra
- Reduce your weight to a bird's, and turn your arm into wings
However, this is not explicitly RAW. The spell has the Aquatic Adaptation mode which explicitly grants the caster a swim speed equal to their walking speed; it doesn't have this for flight. Further, the fly spell is a third level spell, which this use shortcuts to, albeit for one target only.
My question is, would this be a valid use of the spell?
No, for full flying
The Change Appearance portion of the alter self spell says (emphasis mine):
The important part to note is that it explicitly states that none of your statistics change, and you retain your basic shape. Adding wings that would be large enough to allow you to fly is a major alteration to your basic shape (humanoid). I think the portion that covers being quadrupedal sufficiently demonstrates that a major modification in methods of travel is outright denied. Especially since if you can't change your arms into legs (which is a very minor change considering they function similarly), logically you wouldn't be able to change them into wings either. The intent of the spell seems to be for small changes such as:
Skin pigmentation, reshaping ears, eye colour, hair colour, talons, claws, teeth, and other minor modifications. The most major modification is definitely the ability to breath water, but even that simply allows you to extract oxygen from a medium other than air, which is another minor modification.
How I would rule as DM:
I would personally say no to wings, but yes to a bat-like membrane (picture a wing suit) between your legs, arms and body. I would even house rule that you could get half speed flying out of it, and of course, gliding. Since you don't have hollow bones, or a small mass like a bat, that's why I would personally impose the half speed limit. This conforms to the restrictions of the spell and would permit some creative experimentation.