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"In terms of British Airways. How does that work? I transfer from SPG
to BA and place the order through their website?"

Step 1: Go to ba.com, and sign up for a BAEC account (free).

Step 2: Search aa.com for "SAAver" Coach award seats on NYC-MIA nonstops, which AA offers from the three major NYC airports. If available, these seats will show up as requiring 12,500 AA miles, but since you won't be redeeming AA miles, that's irrelevant.

Step 3: If you find SAAver Coach seats on AA nonstops, transfer 7,500 Starpoints to your BAEC account.

Step 4: When your 7,500 BA "Avios" show up in your BAEC account, make a reward booking on ba.com for the NYC-MIA nonstop on AA.

CAVEAT: Transfers from SPG to BAEC are not instantaneous. There is always the possibility that the award seats you found before you initiated the transfer will no longer be available once the transfer is completed.

There are other points that transfer to BAEC faster: Amex MR and Chase UR. And it is also possible to earn BAEC Avios directly, with the Chase/BA Visa card.