Another way to find this information is to do a simple Google search. For example, one could place the following phrase into Google Search: “(product name) + affiliate program”. (Replace “product name” with the name of the product you are promoting.) There is an interesting chrome addon called Affilitizer is available which makes this process easy.
Once you’ve set up your account, do note that Amazon requires you to use product links and generate income from at least three of them within 180 days. If you fail to do so within that time, they will close your account. If you are able to satisfy that requirement, Amazon will review your account as well as your usage of affiliate links once the first sale is complete.