I would look at the transaction on americanexpress.com, click to expand it, and see if BA is identified as the actual seller.
Interesting point that I had not thought of. l found the transaction and it says that the seller will appear as BRITISH AIRWAYS ARC USA on my bill. Does this mean I can go into the BA forum and ask for assistance from "BA refund helper?" Or go direct to BA somehow? I tried this on a previous BA booking and when I called BA, they just referred me back to Amex.
Given that I am entitled to a refund, that is what I want as I am already stuck with a bunch of BA vouchers. If a chargeback can be ended by a voucher as mentioned above then doing one might be risky.