So far, the net indicates no, because Flying Press is listed as Fighting, even though it deals Flying damage and will be x2 against Pokemon weak to Flying, e.g. Grass.
Pokemon that resist either Flying or Fighting are damaged by a x0.5 modifier, e.g. Electric types take x0.5 damage from Flying Press.
Flying Press - Coverage
I guess x2.25 STAB would be OP'd, considering that it has a base power of 80, meaning 80 x 2.25 = 180.