Send people to your TikTok video
Add your TikTok video to every Auto DM as a second button, so people can buy on TikTok Shop too, even when Amazon doesn't have the product.
Yes, your Auto DM can send people to the TikTok video a post came from, next to your Amazon link or on its own: set Button 2 under Buttons in your DM to My TikTok video, and every DM gets a See it on TikTok button. It's one setting for every DM, so you don't change your videos one by one.
Turn it on
Open Settings → Auto DM. On the Facebook card, under Buttons in your DM, set Button 2 to My TikTok video. It saves the moment you pick it, and the Instagram card uses the same buttons. From then on every DM gets a See it on TikTok button that opens that post's TikTok video, under the shop button (which then reads Get it on Amazon unless you wrote your own label). The TikTok button is left out of a DM when we can't tell which TikTok video the post came from, and a video you uploaded yourself has none.
When Amazon doesn't have the product
With Button 2 set to My TikTok video, a video with no Amazon product, or one you marked not on Amazon, still gets its DM, without the Amazon button: it goes with your other buttons, the TikTok button and Button 3 if you set one. If we can't tell which TikTok video it came from and there's no Button 3, no DM goes. With Button 2 set to None, that video gets no DM, so the people who comment get nothing. See When a product isn't on Amazon.
The post itself carries one link
The link in a Facebook caption, a Facebook first comment, a YouTube description or a pin is one link per video: the Amazon product, or your own link if you set one. To post a different link there (a TikTok Shop product link or a brand's website), use My link → Custom link, for one video or every video of a product. See Use your own link.