I am surprised you pay for a premium card like the Reserve and are unaware that it is not a transfer partner to AA. Technically you may (unless it's changed) be able to book via BA or Iberia and fly on AA metal, but I believe you get your points back, not a cash voucher. You may need to read the terms and conditions, and some travel articles. The basics apply across-the-board. Paying $550 a year for a premium card, you want to get value from it, not try to game the system.