No, for full flying
The Change Appearance portion of the alter self spell says (emphasis mine):
Change Appearance. You transform your appearance. You decide what you look like, including your height, weight, facial features, sound of your voice, hair length, coloration, and distinguishing characteristics, if any. You can make yourself appear as a member of another race, though none of your statistics change. You also can't appear as a creature of a different size than you, and your basic shape stays the same; if you're bipedal, you can't use this spell to become quadrupedal, for instance. At any time for the duration of the spell, you can use your action to change your appearance in this way again.
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.
Some people might ask whether alter self can change your weight at all, given that the text says "change appearance" and not "change form". But note that this spell is a transmutation spell, not an illusion spell. The changes produces by transmutations are changes to your form.
Alter Self says: "You can make yourself appear as a member of another race, though none of your statistics change. You also can't appear as a creature of a different size than you."
So, for example, you could change yourself into a dragonborn, which has "average weight" 250lb. It's not clear in 5e what the upper bound is for a medium size creature.
A DM looking for guidelines on the upper bound for a medium size creature might look at the table for 3.5e, which says that a medium size creature usually weighs "between 60 and 500" pounds. Obviously this is just a guideline -- and a guideline from a different edition, at that. Ultimately you will have to let your DM decide.
Best Answer
I think your players need some help understanding the game's fundamental abstractions. To that end, let's address their plan:
Sounds like a pretty reasonable way… to deal 1d6 damage
In reality, human beings have some pretty sophisticated tools for rearranging each other's internal organs in order to quickly cause incapacity or death. One such tool is a "sword."
In Dungeons & Dragons, that awesomely lethal tool does, like, 1d6 or 1d8 damage. Which is also, in many editions, enough to kill a starting character in 1-2 hits.
If you don't mind, I'm going to borrow a bit of text from a prior answer about a similar instant-win strategy using poison:
Something that should kill a regular person can, by all rights, do 1d6 damage in D&D. As other answers have already noted, the Alter Self spell already has a "natural weapon" option that will do just that!