Links that lead back to Amazon are allowed. However, links that are not directly referring to an Amazon domain are not allowed and will most likely be blocked by their Seller Central Messenger filters.
Amazon wants to ensure that the entire transaction and communication stays within Amazon, as explained in the first section of Amazon's Prohibited Seller Activities and Actions (found here), regarding attempts to divert transactions or buyers. This means that the buyer and seller must commit to keep all association and communication inside Amazon's Seller Central system.
We recommend using Feedback Genius' email variables to ensure your message's links are following Amazon's Terms of Service.