I have a Known Traveler Number through Global Entry, and normally get TSA Pre on my boarding passes for US airports.
British Airways is the only airline flying non-stop between my home airport, San Diego, and London. In the past, I've booked directly with them. BA does not participate in TSA Precheck.
The flight is codeshare with several airlines, including AA, which does participate in TSA Precheck. Could I get TSA Precheck by booking through AA using their codeshare flight number?