Hmmmm, you are confusing things somewhat. Let me see if I can give a simple explanation. NOTE: there are a million options and scenarios, I'm just trying to keep it really simple.
1) Wordpress themes - don't pull product feeds and arent designed for that. The theme is simply the color, font styles, layout, graphic elements part of the blog. The theme is the framework if you will.
2) There are some PLUG-INS that let you display other people's RSS feeds on pages of your blog. BUT that will only display products with your affiliate link IF the merchant provides RSS product feeds. Hardly any of them do. Datafeeds yes, RSS product feeds are hard to find.
For instance I use the FeedWordPress plug-in to display snippets from other blogs on my 5 Star blog pages. Example here's Partnercentric's blog on one of my pages.
PartnerCentric Blog on 5 Star Blog.
But again that only works because they give me an RSS feed.
If it was a datafeed it would not work without special software or some coding.
3) There are some scripts you can BUY that convert datafeeds to RSS feeds so you can display them on your blog. They cost 100 - 300 and it's not super simple. There is some cleanup and conversion that needs to be done to make it work. Let me know if you are interested and I can show you some articles on my blog about a couple of the best ones.