Each product, each astore you create has a url, a very long one with your id in it. If you are referring to doing something like buying a domain name like you would for a blog or website, you cannot do it. Amazon may not pay you if you use those bit ly, and other url shorteners either because the system does not always pick them up as the reffering source of a purchase.
Set up A store with products. You have 3 ways listed as to how to get the store on your site or blog.
Or write articles and use hyperlinks.
or use the HTML codes for each product to place in sidebar of blogs.
You can also copy pic of product put it with a blog post. But you can add caption to. So when your write caption, use that for your hyperlink to product with your ID in it,