3rd parties integrate with PayPal or other payment services. And then generally link to a form to input a number.
Twitch doesn’t offer this. The third party market is relatively mature here, and Amazon Pay itself doesn’t really support this sort of payment flow. (Giving money in exchange for nothing, except in the case of a donation to charity which a streamer is not as they receive tips)
I think dist misinterpreted your question and meant you were looking for an API to automate the whole thing. Which doesn’t exist anyway, (generally speaking)