Your gig doesn’t tell the buyer nearly enough, so a user can by it and expect almost anything. Technically you can write unverified reviews on Amazon without buying a product, so you could complete the gig. Amazon reviews of any kind are against the Fiverr and Amazon Terms so you are in a mess. If Amazon removes your review (likely) the buyer might leave you a bad rating on Fiverr. Your gig also leaves you wide open to other bad deals like Yelp reviews, GoodReads reviews, Trip advisor, etc. All of those are 3rd party sites and can get you in trouble.
That still doesn’t leave you completely stranded.
First, I suggest you offer a mutual cancellation to the buyer with a polite explanation that it’s against ToS for you to review on Amazon. If the buyer doesn’t respond it will auto cancel and put a little dent in your account. In this case that’s far better than a late or bad review.
Second, I’d contact Fiverr Customer Support, explain your mistake, and ask them to back you up with a forced cancellation if the buyer refuses.
Third, pull that gig fast for a re-write or replacement. The review category on Fiverr is safe to use if you are very clear. You can write reviews the buyer can post but not offer to post them anywhere. You can also write reviews and post them on a site or blog that you made. Otherwise, reviews are pretty much over on Fiverr.
You can do whatever you want to, really, including completing the gig with an unverified review and risking it all. This is just advice. Note also that Amazon can use you personally if you do it. They probably won’t, but they have used others and they have the right. Good luck.