Hi Mr. Hutton,
I've been doing the Berlin-JFK route for almost 20 years. There is NO WAY you can do a terminal change, security and check-in in an hour.
I don't know what security is like at Terminal 5, but for the delta flights it takes about an hour to get through just that. You won't have to do customs and German immigration until you hit Berlin ... that gets to be an issue on your return trip, when you have to do US immigration.
I would say, to be on the safe side, you need at the VERY LEAST three hours transfer time. The other thing you have to consider is if AirBerlin is going to require you to check-in on site at JFK. I've never flown Air Berlin transatlantic, but this has been my experience with other carriers (PanAm (in 1990), Delta, BA, Continental, United, Air France, Lufthansa, Iberia).
Since, 911, on transatlantic flights to and from the US, internet check in and boarding card issue seem to take place in person, at the desk -- period.
Both Jet Blue and Air Berlin are great airlines ... but make sure you relax and give yourself plenty of time to make the transfer ... like I said, three hours is the minimum, and five is probably best.
Best regards and safe travelling, Taryn Toro
No Way