Maybe this will help someone. I wanted to pay my Amazon Store Card through Bank of America’s bill pay system and it wanted the card’s zip code. Anyway, if you call the phone number on your card, you can say “talk to representative” during the automated system to get to a real person. I’ll save you a couple minutes.
When inserting the pay to account in your bank, name the account “Amazon Store Card-gecrb”. The rep told me to name the account with the suffix, I guess it could be important. Put in your account number and alias as usual, and the address is as follows, though you may only need the zip code:
PO Box 960013
Orlando, FL 32896-0013
I hope that works for you!