I counted four red flags before you even got to the words "Gift Cards", that's worth ten red flags. Don't ever respond to any unsolicited emails no matter who they are from. Don't even click on the email itself or hit the 'unsubscribe' button. That's most likely a virus waiting to attack your computer.
It's your Amazon account, go to the Amazon website and look at your account, are there any purchases you didn't make? Probably not, problem solved, delete the email. It happens probably 10,000 times a day. If you want more backup, go to your credit card account and see if there are any charges you didn't make. In two minutes you found all the information you needed on your own, and you now have peace of mind and some crook doesn't have your information because you did it the right way.
Just because you see a logo, or some links, or words, doesn't make it real.