I don't see the point in getting to JFK before about 16:30, or 16:00 if you really do get worried about these sort of things. The time check-in opens can usually be found in Manage My Booking, flight line for JFK-LHR, check-in, other ways to check-in. Currently this is offline unfortunately. But baggage check-in starts about 12:00 hrs, varying slightly according to the timetable and Daylight Saving.