Amazon affiliates will not let you put their links in emails. In fact, many affiliate programs don't let you do that, and they won't count a click/conversion if it comes from email, or worse, they'll ban your account. Some affiliate programs will let you do it if you get permission from that brand's affiliate manager first (I successfully did that for 1 brand I wanted to feature in my email newsletter to my mailing list).
So for email, you probably need to find an affiliate program OR ad program that's targeted toward owners of mailing lists, or else look at affiliate programs you're interested in one by one to see if their TOS allow you to put links in emails.