[RPG] What paragon paths and epic destinies grant wings or flight

Demigod is pretty darn good. It's still (even post errata), considered one of the best Epic Destinies that any character can take. The +2 to two stats, and regen are just that good.

However, if you want to go a different route, the other one you've chosen is well rated (though less than Demigod).

One you may qualify for being that you've got some MC Ranger going on is Deadly Trickster. If you don't qualify, you might be close enough to build for it (need 21 DEX or CHA and training in one of 4 skills).

It offers some very nice reroll, power recovery and denial options as the various features and I'd recommend it for your character if you qualify.

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.