Welcome, I am Cory. Thank you for asking your question today.
Please login to your Amazon account at http://www.amazon.com
Please go to https://www.amazon.com/gp/wallet?_encoding=UTF8&ref_=ya_wallet to see the payment Wallet.
Click on the old payment and delete it completely.
Click on Add Credit/Debit Card and add the new payment.
You will be able to use it on the Kindle.
Please let me know if you are able to fix this issue with the instructions I have given.
I am following with you to see if you fixed the payment info or if you need further help with this.