The actual flying time between JFK and HEL is usually about an hour less than what is says on the schedule. However, the plane might wait quite some time at the tarmac in JFK before take-off. Longer than any AA flight I've ever been on... However, my experience is that delays are relatively uncommon on this route.

HEL is practically deserted when you arrive. Shouldn't be any lines at passport control.

If the BUD flight leaves from a jetbridge gate (no bus), they will start boarding perhaps 20 minutes before take-off (never the 35 min that is printed on your BP).

I would say that if AY6 touches ground more or less on time, you will be safe. A delay of, say 15 minutes, should be no catastrophe since you are in J and deplane early.