This feature is available with some paid plans
You may notice that links created from Amazon.com automatically use the domain amzn.to. This is due to a feature called auto-branding, available on Enterprise accounts.
When a company has enabled auto-branding, any links created from a site associated with their Bitly account default to the domain of their choosing. In this case, Amazon.com auto-brands to amzn.to.
Customizing auto-branded links
If you have a custom domain, you can choose to use it when you shorten a link from a website that uses auto-branding.
Once you've created an auto-branded link, though, it can't be customized. This includes the back-half of the link.