You will be able to use the BA F lounge in JFK (CX doesn't have its own lounge), although some say the adjacent J lounge is nicer.

In Hong Kong you can officially use only the J sections of the lounges (The Wing or The Pier); some may say you should try to talk your way into the F lounge on the basis of your inbound, but I wouldn't rate your chances highly. The Wing is much more "open" feeling and the Pier is cosier. There's no difference in food or drink offerings between the two J lounges (the F lounges have a much nicer full buffet restaurant). I would generally use whichever is nearest my departing gate.