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As far as I know AMEX card is supported by Stipe. It says also on the Stripe support page.
It could be about a different problem.
Have you retried it already? Perhaps some typo on the card details was the culprit.
I could not do a proper test since I do not have an Amex account to test it out, but can you please check again. You can also take a screenshot of the problem and share it on your response. This way we can have a visual of the problem when it happen.
Let us know if issue remains.