Hi JoAnn,
I booked our own air for FJORDS using AA miles. We flew BOS to LHR, transferring to BA for the CPH leg. We did the reverse on the return. Our bags made it both times. As I think Leslie said, tags were put on our luggage in both BOS and CPH saying "fast transfer". When we handed our boarding pass to the BA ticket agent on the LHR-CPH leg, she asked if we had checked any luggage. When I said yes, she asked to see our checked luggage receipts. She put the numbers into her computer and when I asked if there was a problem, she said no, she was just making sure our bags were on the plane.
Friends of ours on FJORDS also did their own air using AA miles, transferred through LHR to BA and had no problem with their luggage either.
My best advice to you is to pack a carry on bag, at least on the front end.
Good luck-
Kathy