Under EU reg. 261/04 as the traveling commenced in EU.

Good luck in getting AA to accept EU comp. for a downgrade of the ORD-OKC segment (i.a. a domestic US flight)

Anyway, under EU reg. 261/04 the comp for the downgrade will be 75% of the points/miles for the ORD-OKC segment. For an BRU-LHR-ORD-OKC itinerary that will be close to 10% of the miles/points used + taxes as the ORD-OKC distance is less than 15% of the overall distance travelled. You should consider how much time/efforts you are prepared to put into this, to get a 10% refund. I can almost guarantee you that AA isn't going to make a refund voluntarily; main argument is that you could have waited until 4 F seats were available, but the party preferred to get the earliest flight to OKC albeit in Economy.