Getting a refund from Amazon can be difficult. They do not share any user information with app developers. This is great for user’s privacy but it means as an app developer we have no way to issue you a refund.
Amazon has a No Refunds policy concerning application purchases. (Here is a link to Amazon’s Digital Content Returns: Amazon Digital Content refund policy.)
However, if you have been unable to use the app or it has disappeared from your account they ask that you email them explaining the problem. Here are two links to Amazon Customer Service, one is a general customer service link the other is for Kindle Fire support. There is also a US support # for Kindle Fire users.
While I recently heard from a user saying Amazon was quick and helpful you may need to be persistent. You may need to remind them that Amazon collected your funds by charging your credit card, the app developer did not. As the app developer we have no record of this sale.