When flying creatures take to the skies (which connects to streests in both Arkham and Dunwitch) from Dunwitch (which has no monster limit) do they count against the Monster limit in Arkham and spill over to the outskirts.

Yes.

Flying monsters in Dunwich can be a real pain if you are trying to keep down the terror level.

On the other hand, at least flying monsters in Dunwich will never enter a vortex, and that's a quick terror-up.

But yes, flying monsters in Dunwich, Kingsport, and assumedly Innsmouth all go to the Sky box in Arkham when they fly--this means they will count against the limit and may go to the Outskirts instead when they take off.