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The documentation at http://login.amazon.com/documentation/combining-user-accounts talks about the steps needed to link a customer’s Amazon account with your website’s account management system. These ‘account linking’ steps are different from what is required for a website to login/logout a customer on their website.
The Login with Amazon Developer guide captures the steps required to logout a customer from your website. Please refer the “Logging Out a
User” section here - https://images-na.ssl-images-amazon.com/images/G/01/lwa/dev/docs/website-developer-guide.TTH.pdf