Make sure you have previously logged in on https://developer.amazon.com

To setup Amazon social login, go to https://developer.amazon.com/loginwithamazon/console/site/lwa/overview.html and click on Create a New Security Profile 

Fill out required fields such as the  Security Profile Name, Description and Privacy Notice URL

After the new Security Profile is created, click on the Manage button on the right and select Web Settings

In Web Settings tab you can find your Client ID (1) and Client Secret (2).

Provide the following URL as Allowed Return URLs (3): https://yourwebsitedomain.com/wp-login.php/?action=social_login_authenticated&provider=Amazon

Adjust domain to match your website domain.

Enter the Client ID and Client Secret keys into Social Login plugin configuration and you’re good to go.