Does not always work with a combined itinerary with different carriers. However, you should have both an AA record locator and a BA reference, so go to each site in turn and check in.
You definitely want to check in any AA flight on the AA site as it will print eg. 'TSA pre-check' on the boarding pass which BA cannot do, or any other fast track entitlement, for onward connections in the US.
I always do it that way and generally save long lines of checking in/ security as well as not having to take laptop out, shoes off, jacket off...so much less hassle
Good luck!