If you're planning on purchasing business/first on BA then you should first see if there are through fares on BA/AA to PHX which allow transferring at DFW. They may be way cheaper than combining two fares.
If you end up looking to buy - just select first class with restrictions on AA.com and the cheapest (usually so -called 'instant uphgrade') fare will be offered.
You will earn miles/TPs separately for the BA and for the AA segments.