From my friend Nils, who served with Army Intelligence (and assures me it's an oxymoron) Fuckin' A is short for fucking affirmative, meaning a rather extreme yes.
Nils is very victiorian about many things, among them vulgar language when ladies are present. But when I mentioned that the villain of a novel I'd written was a crooked right wing politician, and I intended to keep him on the right, he shouted with verve and enthusiasm, F***in A! Followed by an appology.