Can Ynnari take Flyer Wings?

And if so can those Flyer Wings be part of an Air Superiority detachment?

No, apparently not.
As it stands, the ONLY Detachments and Formations which can take the Ynnari Faction are those listed in the FoBT book.
THere is nothing to stop you allying in a FLyer Wing, but it will have to be an Eldar or Dark Eldar FLyer Wing, using the rules for those Factions.

Just once I'd like to learn something about this new faction that *doesn't* piss me off.

You've made it abundantly clear that you don't like the new faction so why would this annoy you? I assume if you don't like it you're not playing it?

I wanted to bring a detachment of Hemlocks and Razorwings that would allow me to bring everyone on the board at the same time and heavily manipulate reserves with my Air Superiority detachment bonuses. However the fact that I cannot bring Hemlocks and Razorwings in the same detachment means I would need 2 detachments and they would not come on with the same roll. This was one instance where having them in the same faction would have been really really helpful.

Even in the same detachment, if they are not a single unit, they would have rolled separate reserve rolls to enter the field. I don't have DftS book, so I don't know if there is a kind of flyer formation of DE and Eldar mixed that comes in a single unit... But if it has, just take it. If not, I don't see the benefit of having them in the same detachment.

The DftS detachment says explicitly that the 1-3 flyer wings can roll as if they were one unit to come on, allowing up to 12 flyers to come on at once. That is the benefit. And no there is no Eldar/Dark Eldar detachment.