So I think it depends on the nature of your first flight. If flying BA1 you can check your bag through to the final destination (either on a single itinerary or on to a OW partner). A very small number of US hubs also allow through checking of bags if I understand correctly.

In your case I would check to the first point of arrival, then retrieve and recheck with AA who will probably allow you to through check to DL (as I think this is more normal in the US).

You will have no joy with BA checking on to DL so AA is your best hope for a single collection and recheck.

I haven't done this myself so it might be worth checking AA's conditions for onward checking of bags.