Is 1 hour enough for a connection at JFK?

At JFK, it depends entirely on whether you're changing terminals. JFK has six terminals (1, 2, 4, 5, 7, 8), and unlike many airports, they are NOT all connected airside. If you need to change terminals, you must exit security, take the AirTrain between terminals, and go through TSA again — a process that takes 30-45 minutes on its own.

Same terminal, same airline: 1 hour is usually fine if your first flight is on time. Terminal 4 (Delta's main hub) and Terminal 1 are relatively compact. Walk times between gates in the same terminal are 5-15 minutes.

Different terminals: 1 hour is almost certainly not enough. The AirTrain ride between terminals is 5-10 minutes, but you lose time exiting, walking to the train, riding, walking to the checkpoint, and clearing security again. Delta operates from both Terminal 2 and Terminal 4, and while there IS an airside connector between them, other terminal pairs require the full exit-and-re-screen process. The airline MCT at JFK is 90 minutes domestic with terminal change and 120+ minutes international.