My guess is that the "flying part" is simply just a fancy way of teleportation. you call your giant hawk or whatever, and fly to some position in a few seconds. *Link flies away, white screen, Link lands*
Maybe we can watch as we fly above Hyrule, takes a little longer to reach that destination, but it would be way cooler.

Now getting to your, I must say quite cleaver ideas, I think the last one is the most fitting. And also the most possible to become reality. Hanglider woud be awesome though. But as you have to start from a high point, it would be rather useless. Unless it is a one way transport, getting to that sky temple and back.

In the second trailer, we saw Link riding on a bokoblin boar. Is it possible that he could take enemy flying steeds as well(if there are any, and I'm not talking about those pteranodons)? That would be awesome.