Military Discount and using a gift card to pay

Had the same issue. Switched to chrome and it worked.

Here is the regular store payment info and terms which may be helpful. I tried to get to the same page for the Apple Military store, but was unable to because I am not military and therefore could not access the store. You will need to do that yourself; once you've accessed the store, look for payment methods at the bottom of the pag and see if they accept gift cards.

Payment, Financing, Refunds and VAT - Shopping Help - Apple

Yes! This just happened to me today. I was able to get all the way to the final complete order page - we were buying online due to the military discount is only online, and using 2 gift cards and credit card - to pick up in store. We were at the store doing it with a rep who confirmed there were tons of the device in stock, and it would change to only being deliverable (which costs an extra $80). There was no way to change it to pick up in-store (tried different stores and different pick up days/times) and tried multiple times to try to get it corrected. Nothing would fix it. Insanely frustrating. Also was transferred 4 times on the phone and no one seemed to know why the problem was happening or any solution of any kind.

There’s clearly a glitch in the system. Took us ten times to get it right. Just keep trying or call apple support.