Quote Originally Posted by SE
We’ll be introducing flying mounts, and it will be possible to freely take off and land. You’ll also be able to fully control them on x, y, and z axes. However, you’ll need to "attune" to areas first, so you won't be able to fly around as soon as you obtain a flying mount. Think of as you needing to explore each area beforehand. It will be possible to fly in every area except Ishgard.

It will not be possible to fly in A Realm Reborn areas, as the maps were not originally designed to allow for flying. We might address this one day, but for now we would like to focus our efforts on adding new areas.
http://forum.square-enix.com/ffxiv/threads/230605