I would've preferred "Wind" or "Aerial" type, Flying infers that the pokemon has to always be airborne. "Fighting" isn't "Martial Art" type, and not all Fighting pokemon are designed with typical martial art traits in mind i.e. Sawk compared to Breloom.
Not being called Flying would also allow grounded Flying pokemon, themed around things like turbines, bellows or generally expelling wind in some way without having to be levitating off the ground.
and it would negate the stupid all-Ground immunity. Mud bomb not hitting Flying types will forever be retarded