Flask Logout All Sessions of a Specific User
As Artiom said in his answer, Flask-Login by default uses Flask session which is client side, and you won't be able to delete all those cookies from other clients.
However, there is a way to prevent other clients from logging in. Flask-Login relies on user_loader callback function to fetch the user from your cache, this function gets called on every HTTP request coming from the user's client. 
What you can do is on logout, you delete this particular user from this cache. That way when any client (phone, other browser,etc..) used by this user try to access your page. Flask-Login won't find the user in the cache and will redirect them to the login page.
When logging out a user with Flask-Login, is there a way to log out all sessions that user may have (Ex: in different browsers, different devices, etc)?