How to save username or channel id of our website user in our database to stream their channel on twitch

Logout of what?

Your website? That depends on your session manager that you have for your website

The API doesn’t have a “logout” method since you never logged in.

The API has a “revoke” access key method, but generally you don’t need to use that, since you probably want to store the users access and refresh tokens in order to continue to use their access keys