I understand you need to book flights on an Amex card, not particularly your Amex Plat card. I've had this confirmed a number of times on the phone to Amex customer services. However the card T&Cs specify that the flights must be booked on 'the card' which means the Plat card. Obviously if the airline doesn't accept Amex, Amex will honour the claim.
However, I've booked flights on my BA Amex card and claimed for lost baggage against my Amex Plat policy and had no questions or issues, and Amex paid out.