Apparently Zinio is having some trouble. Their app is APPROVED for the Fire on the Amazon App Store, but you can't install it. At least for now.
They have a link to directly download a Fire friendly version here:
http://www.zinio.com/help/index.jsp
They are, next to Amazon, the nicest company ever. They even give you welcome credit, free issues to read while they fix broken ones that you report, and some other freebies that come up sometimes. I'm almost at my second year using them. HIGHLY RECOMMEND!