Guys, I apologize. This has been a very busy time of the year for me traditionally.
I have flown out of JFK three times in the past 18 months with pistols on a NYS (not NYC) issued pistol permit.
All three times have been relatively uneventful, but more or less time consuming. Before doing it the first time I spoke with a Lt. Mancuso from PA watch command to discuss the procedures. Remember, the airport falls under the control of NY/NJ Port Authority, not NYC. When I called NYPD I was greeted with abject ignorance. I ended up calling my counterpart in the PA and he put me in touch with watch command.
Have your pistol unloaded and I would recommend banded through the barrel and ejection port, or through the magazine well and ejection port. This shows the airline personnel as well as LE that the firearm is in an inoperable state. Have the case locked and inside a locked bag at all times. Do not remove the case from your luggage or unlock the case until you are directed to. The airlines apparently may set their own rules now as to whether ammunition may go in the same piece of luggage or not. Check with TSA and your airline in advance. You do not want to have only one checked piece of luggae and them tell you that the ammo must be in a seperate piece of luggage and you are forced to surrender it.
I advise the following tact when speaking with counter personnel. Before you declare the firearm, request someone from TSA come over because you need to make a decalaration. TSA could give a damn about whether your permit is NYS or NYC or not. While you likely won;t have a problem with a PA officer, your chances are much better for a smooth sail through security if you deal with TSA. The one time I had to deal with a PA officer he got a little antsy about me not having a NYC permit - he might have come over from NYPD. I calmly explained to him that I had spoken to watch command and gotten the procedures to follow and here was my NYS permit along with my government credentials (these put him immediately at ease, an advantage you might not have). He wrote down my permit number and the serial numbers of the pistols in his patrol pad and checked them against my permit. When he saw all was in order he became quite helpful in speeding through the rest of the process. Just remember to be respectful, address the officer as Sir or Ma'am and be at ease with the process, that will go a long way to putting them at ease.
Do arrive early. Do have your permit readily available and there should not be an issue. If you run into problems, ask for them to call watch command. You might want to yourself in advance and provide them a courtesy call with your flight number and such and tell them you want to make their job less stressful. It really is amazing how far a little kindness and consideration will go.