I wish more people knew about fraud protection and how not to trigger it. If you want to pay in an unusual way, ask support if it's allowed or causes issues.
If you just try and imitate the average customer you will almost always be on the happy path, but ordering multiple books with multiple cards in a short period... I think that would trigger any decent fraud protection and not just at Amazon scale.
For most services (I'd assume even Amazon) they likely wouldn't be able to tell you what would trip their fraud detection. Most of the time fraud detection happens at the payment processor or issuing bank level, and even if it is detected directly by the service, usually the support department doesn't have much access to the fraud department, and fraud departments are usually very protective around details of how they detect fraud.
To be fair, it seems like their only option was to look like someone running stolen credit card numbers, due to how two systems outside their control worked—the work payment system that issued one card number per transaction; Amazon not letting you buy more than one ebook at a time.
If you just try and imitate the average customer you will almost always be on the happy path, but ordering multiple books with multiple cards in a short period... I think that would trigger any decent fraud protection and not just at Amazon scale.