Baobab... to get from LGA to JFK your best bet is to take a cab. It's also good to make sure the cab takes you there (some whine about going that distance -- but city law says cabs cannot refuse to take passengers to where they want to go.)
Does British Air (if you are taking them) have a shuttle bus or can arrange transportation.
I'm dreading going to JFK end of month for my VEGAS trip... I do NOT like the NYC airports!