Curious. It is dual type so I was wondering. Also, does it gain double STAB.
It hits Normal, Grass, Ice, Fighting and Dark type Pokemon for super effective damage. The other type matchups can be found here on Bulbapedia.
And no, Flying Press does not give Flying/Fighting type Pokemon double the STAB bonus. Since it is a Fighting type move, only Fighting type Pokemon receive STAB from it; the Flying damage is merely a side effect.
I thought of the same question and all I could find was the snover line. The fighting part beats the ice part, and the flying part beats the grass part. Hope I helped