This expression became a term of encouragement after the following exchange in a live New York local Fox News broadcast at the end of the weather report.
Ernie: "It takes a tough man to make a tender forecast, Nick."
Nick Gregory: "Well, I guess that's me!"
Ernie: "Keep fucking that chicken."
The first line is a parody of a commercial for Perdue chicken from the 1970's, in which Frank Perdue uttered the tag line, "It takes a tough man to make a tender chicken." "Keep fucking that chicken" was the punchline of a joke of the same time about how Perdue did it.
"Keep fucking that chicken" (KFTC) is a phrase coined by television anchor Ernie Anastos during a live broadcast of the Fox 5 New York local news. It is presumably a phrase of encouragement similar to keep on truckin, only with a more pronounced and colorful air of defiance.
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.
Adam: I could be making more money at another job, but I like the work I'm doing now.