I had a heck of a time with this. I tried their veteran prime discount data entry page and got back errors three times. I called Amazon and it took about 20 minutes of phone time and six emails back and forth to finally get the "authorization" to get the discount.
Hopefully this won't happen to everyone.

I’m in the middle of errors and emails!
Hope I can get it done!

I kept getting error messages, contacted the email address in the error message, got a reply that said "try again."

Tried again, back to the same error message. Rinse, repeat.

Finally, on about the sixth go-around, it worked.

Royal pain in the ass. I probably went through fifty dollars worth of blood pressure meds, to save forty dollars on Prime.

After a couple of emails, it worked!
Thanks for the info!

I'm in... thanks.

Thanks for the reminder.

Odd, it would not take any of my info, 3 strikes and I was out! I did do a chat with Amazon and got an email address to complain to, I guess they are checking, but who knows.

It was like trying to log into the VA health system...