I have a free WordPress website with 1000-2000 visitors/month. I was trying to place Amazon Affiliate ad links last night and failed/flailed mightily. I would paste the links into my posts in the HTML mode, switch to Visual mode, and could see the image. However, every time I tried to save or update the post, the image reverted to the gangly hyperlink. As some suggested, I tried cleaning the links of any formatting from the copy and paste with text edit. No dice.
Hypertext Markup Language (HTML) is the standard markup language for creating web pages and web applications. This step is important to keep your costs down and still get what you want. If you're not familiar with basic HTML and basic concepts about running a website, invest in the time to learn; it will be well worth the outlay in the long run. Even if the site is basically a template for you to use, you're still going to need to know how to insert images, create hyperlinks, and do some text formatting.
I recognize that the list above is short; however, that’s because Amazon affiliate marketing really doesn’t require a specialized theme in order for it to work well (unless it’s one of the unique cases noted in the themes above). Instead, you’re better off using WooCommerce if you want to build a full affiliate store or simply stick to the WordPress theme you currently have and add affiliate plugins to the mix.