The ability to redeem the voucher, which is obtained by mail when you purchase the game controller is a little hidden. "Buy now with 1-Click" on the product page below the large -button, there is a link "gift voucher or promotional code to redeem and show balances" - there you can enter the coupon code in the mail, the amount is then when shopping deducted automatically.
Whether the game is actually what can still come on - so far it does not appear on my TV Fire ;-).
Addendum: In Fire TV menu under "Settings -> My Account -> Synchronize Amazon content"
