We're sorry! At the moment, Curve doesn't support Amex.
We are having ongoing discussions with American Express regarding their relationship with Curve and the potential for us to work together in the future. They're a big company so they're unable to make strategic decisions as quickly as we can, and as a result there's no firm date we can attach to any change to the current situation.
Naturally our goal is for Curve to work with all payment cards across all markets globally, and beyond American Express we're in discussions with other partners to bring them on board.