It offers DFW and ORD.

For some reason the DFW option books a lower class fare on the AA segment, at least it did for me last week booking outbound on 1st May (book in CW on BA, get economy on AA, book in F on BA, get Business on AA). Strange, as there obviously is availability in AA Buisiness so why the Economy seat?

So I booked via ORD. Which has a BA FLounge and an AA Flagship lounge anyway.