Aonuma said that Link wouldn't fly, but that doesn't necessarily mean that there won't be flight in the game, if you know what I mean. He said something along the lines of "Link won't be flying around like Pit from Kid Icaurus". This can be interpreted in different ways. To me, it means that Link won't be doing the flying himself (e.g. with wings or like superman), but it's still possible that there will be flight gameplay via some sort of mount or whatever. Heck, if you remember that quote from awhile back, Aonuma told his kid that in a future game Link would fly in the sky, so I'm still 90% positive that there will be flight gameplay in this game.
As for how it works, I think the SS girl will transform into some sort of bird and carry Link on her back.