No. Amazon's policies do not allow any marketing or promotional material, including coupon codes.
FeedbackFive does not include any built-in option for adding or generating coupon codes because the Amazon Communication Guidelines say that sellers may not send any promotional materials, including coupons, through Buyer-Seller Messaging.
Also, Amazon’s policy prohibits offering any type of incentive or reward (including a coupon code) for leaving, editing, or removing a product review or seller feedback.
For more on what content you can include in emails, see Are My Emails Compliant with Amazon Policy?