Scootaloo: “Do you think I could be a princess someday?”  
Twilight: “Sure, you can be the goddess of all flightless birds!”  
Scootaloo: “Um… Will I be able to fly then?”  
Twilight: “Of course not.”

Scootaloo: “Twilight, is Rainbow Dash giving you flying lessons too?”  
Twilight: “…Yeah.”

No Scootaloo there is no chance of you ever being a princess. You need a horn for any chance of that. Some ponies were just born with more opportunity. Tough luck.

I’m REALLY hoping the only reason she can become an alicorn is that Celestia is awakening the Element of Magic’s full power….wait…
 
…now that I think about it, this is starting to make the idea of Princess Twilight BETTER!
 
THINK ABOUT IT!
 
The element of magic is a CROWN, what else would she have become but an alicorn when it awakens. That means when the other elements awaken respectively, it will be even MORE awesome cause it will be something new and unique to each of their non-crown necklaces…AND it was already established for the Discord episode the elements belong to them now!!!
 
….Season 4 is starting to look more promising. Spread the word everyone :D

@Sjogre  
Even still, I think she’d view flight as impractical since she already knows how to teleport. Of course Rainbow’s probably going to want her to learn how to anyway, and I can list off the top of my head two reasons why.
 
-What if your magic is acting up and you can’t teleport?  
-What if you need to catch a pony who’s falling? (Twilight would probably shoot this one down with “I’d just teleport that pony right next to me.” or “I could just catch them with magic”)
 
And let’s not even get into Rainbow possibly teaching Twilight how to manipulate clouds.

Given the way that this has been described, I don’t think that Twilight’s magic is getting a boost.

@Background Pony  
As much as I hate you normally. (If you’re the BP that I’m thinking of) You’re most likely right.
 
But I still don’t see Twilight using her new wings that much. She won’t if her teleport range is going to increase as much as I think it is.

Even a unicorn will fly before you do.