IMHO 3 hours isn't long enough.
There at least 3 significant risks.
The first is that your BA
plane might be delayed arriving at JFK
, this could be 1 hour, 2 hours, half an hour, who knows?
The second is you may be delayed at immigration, more likely if it is a BA
B744, and thirdly if you miss your B6
flight it will cost $$$$ to get another.
Seriously consider buying a through ticket and having a B6
experience on your return journey.
I connected at JFK
in November, the experience was so bad that I have decided not to do it again, with or without checked luggage.