I've flown Delta from JFK, but I'm fairly sure it was international. In any case, it's a massive airport and you're gonna be clocking some serious time from place to place, so, especially with so many transfers, it might be worth it to check your bag.

(FWIW, I have vowed to, wherever possible, only fly JetBlue ever again so long as I live in NYC, because T5 at JFK is a thing of supreme beauty, complete with such amenities as legible signage, free wifi, and edible food. I have flown other airlines since discovering this, but not by choice.)