I would like to pay for my subscription with a gift card. How do I do that?

• Buy a gift card, physical or electronic.
• Redeem the gift card to add balance to your Apple ID account (like store credit).

Check your Apple ID balance - Apple Support

• Apple ID account balance will be used first, before other payment methods (if you have those), for any apps and services tied to your Apple ID account.

Note that you will have to subscribe on a different device than Fire TV, as in-app purchases for Apple services aren’t currently supported on Fire TV, afaik. Once you have the subscription, you can use it on Fire TV.