Currently Amazon does not support the use of it's gift cards via 3rd party websites such as WaterFiltersFAST.com.
See Amazon Giftcard Terms Below:
Gift Cards must be redeemed toward the purchase of eligible products on www.amazon.com, or its affiliated websites www.endless.com, www.myhabit.com, and fresh.amazon.com. Redemption of Gift Cards on our affiliated websites is subject to change in our sole discretion. Purchases are deducted from the Gift Card balance. Any unused balance will be placed in the recipient's Gift Card account when redeemed. If an order exceeds the amount of the Gift Card, the balance must be paid with a credit card or other available payment method. Amazon.com may provide Gift Card purchasers with information about the redemption status of Gift Cards that they purchase. To view Gift Card balances, visit "Your Account" on Amazon.com.
When using Amazon checkout any payment method attached to your Amazon account is available, with the exception of Amazon Giftcards.