Bags will not be checked through. You will have to reclaim and recheck them. This is standard for USA arrival. You are transferring to a domestic flight and the second sector has no procedure for screening international baggage so it has to become domestic baggage. This won't be a problem, immigration will take longer than it will for the bags to appear and the recheck is very close. Your connection time is sufficient. It should work just fine.
Also, re the comments about oneworld and interlining baggage -yes, you'd think that is how it would work. But, I see the OP is travelling on BA who have a foul attitude to such things. They have a clear checkin staff directive to not to transfer baggage EVEN TO another BA flight unless all travel is on one PNR/Ticket. No exceptions. Not even for Gold Card holders. Not even if you bought both tickets from BA. Just one of the many reasons why I have given up flying with them.