People have tried this idea before and it's never gone down well. There were those old Safari search plugins that injected Amazon affiliate links into the results, or otherwise replaced existing ones with their own. That caused outrage.

The other thing is, I don't want my experience on Amazon to be modified by the things I type into my OS's search box, which I would expect to be private. What if, in a fit of loneliness, I search for my porn directory, then get a bunch of related items appearing on my Amazon front page?