You need to disclose those affiliate links
> It should be placed near any affiliate link or product review in a location that customers will notice easily. They shouldn't have to hunt for it.
Additionally
> the Operating Agreement requires that the following statement clearly and conspicuously appears on your Site: "As an Amazon Associate I earn from qualifying purchases."
A small bit of UX feedback - when I type a search query that has no results, nothing happens. At first it made me think that the search form was broken. It would be better to show some kind of "no results" result to make it clear that the search has actually been performed.
I'm not in the market for a new pair of running shoes, but the site looks great - and I'm always happy to see more things being built in Elixir and Phoenix. Keep spreading the word!