Yes they do (this was news to me). For Transactions < $10:
1.5% + $0.01 for Amazon Payments balance transfers
2.0% + $0.05 for bank account debits
5.0% + $0.05 for credit card
They also appear to support payment aggregation, which is another method of making micropayments via credit card profitable.
https://payments.amazon.com/help/Amazon-Flexible-Payments-Se...