There is no true "first class" (on a F/J/Y) equipped AA or BA aircraft that will get you to Milan. Thus, the computer will only sell you up to a J ticket on a single award (USA-MXP on AA, USA-LHR-MILAN on BA), as there is an aircraft combination that would provide J service all the way to your end destination.
If you want to book a F award, you will have to book a multi-city:
Ticket 1: USA-LHR (in First) On day 1, obviously an overnight flight.
Ticket 2: LHR-MILAN (In BA Euro J), On day 2.
This will be 2 separate award redemption.