Most of the majors have interline agreements; I'd be surprised if BA and DL didn't. The main problem is having the tickets on different reservations. BA may or may not tag the bag through to the DL flight if you show them the DL reservation. My guess is they won't.

And if you miss your connection, you're on your own. DL is under no obligation to rebook you if the BA flight is late.

You will have to claim your bag to go through customs, but if it's already tagged to your destination you just have to drop it at the recheck desk. If it's not, you'll have to see a representative to get the tag applied.