Installation Problem: No Plugin Found

Thanks for raising the issue with us, chasman.
In order to reproduce this error, can you kindly let us know:
a) The WordPress version your website is running on?
b) Did you try following the ‘recommended’ plugin installation method explained on our Github site (https://github.com/amzn/login-with-amazon-wordpress)?

The issue that was causing that installation failure has been fixed. You should be able to install directly from the plugin search now.