The chicken being fucked may be an actual chicken, could be pejorative slang for a woman (i.e. chickenhead), or some other metaphor for an object of desire or enjoyable activity. In any case, KFTC seems to be a gesture of support to the recipient to continue doing whatever it is that they're doing, despite what others may say, so long as it makes them happy.
Bob: Whatever, keep fucking that chicken.
Dick: I guess that's me...
Ernie: Keep fucking that chicken.
Dari: *googly eyes*