Search for sellers who accept "American Express Serve" or "Amex Serve to Serve" transfers.
Buying with prepaid cards is one of the most expensive ways to get Bitcoin due to high "convenience" markups and potential cash advance fees.
This is the most reliable method for using an Amex Serve card. You aren't buying from the exchange itself, but from a private seller who accepts Serve transfers.
Are you looking to use the at an ATM, or are you hoping to do a Serve-to-Serve transfer to someone online?
You will almost always need to complete a Know Your Customer (KYC) check, which involves providing a photo of your ID.