The "issue" ( I can't find a better word for it), was never really making the animals fly. We know that the engine supports free flying in a 3d space because Planet Coaster had free flying pigeons. The same goes for JWE, they can perfectly fly outside the enclosed space.So firstly we would need to create closed habitat with proper roof (no holes). Add flying space just as we do with water. It could require places to sit and rest. So climbing=sitting elements.
The two major hurdles they had to jump through were making an enclosed space as boundaries and not let animals fly into each other. Now JWE2 clearly shows that they found a way to create an enclosed space using the new aviary tool, which makes me think that the aviaries build in Planet Zoo will most likely also be a kind of fence based tool. Of course I assume that it's going to be with more complexity as JWE2 is often dumbed down a bit.
So whilst I don't think flying is just "swimming in the enclosed space", I do think they were able to use something else that they made for swimming and that is having animals navigate in a 3d space whilst avoiding each other. I think they mentioned in the devlog that hurdle specifically was one of the harder things to do do, but now that that's out of the way the same base algorithm will probably be used for flying.