I regularly fly with guns, as I shoot competitively for a hobby. =)
Delta has been quite good with firearms, same with Frontier, Spirit and US.
FOPA covers you... however...
UNLESS YOU HAVE A NYC CARRY PERMIT.... DO NOT travel through JFK.
Many national champions were arrested. NY Port Authority cops do not care, it is not their job. They will arrest you under orders from bloomberg, and then it will get tossed in court.
It is a gamble.... especially since a nervous check in counter staff will call PANY cops. TSA is not an issue.
I have NEVER been hassled by TSA at any airport, and in most times.... we have good chats about my guns and what I shoot. =)
If you want to discuss, shoot me a pm.