Your Facebook posts carry one product link. Which one depends on the option you chose under Product Links on Facebook in Post Settings.
With Native Link on the Video
It's always your Amazon link. Facebook's Affiliate Partnership program only allows the Amazon link as the Shop button, so Amazon can't be turned off in this mode. Your TikTok link and Custom Link aren't lost, because you can still send them by DM. Here's how to use a caption link and DMs together.
With Link in the Caption
It follows the settings for that video.
Amazon on → your Amazon affiliate link.
Amazon off, with a custom link added → your custom link.
Amazon off, with no custom link → the TikTok link.
To link to a brand's own site, turn Amazon off and add the custom link. To send people to the TikTok video, turn Amazon off and leave the custom link empty.
Where do I change it?
On your Home dashboard, in the Amazon Product column for each video. Changes apply to every video with the same product, past and future, so you only set it once per product. The same settings control which links go out by DM, so your caption and DMs always match.