The instagram API authentication page does not have any information on how to log out a user: On an iOS app using the API, how am I supposed to allow users to log out?
To logout the user you should only delete the token. If the user doesn't want your app to access their data they will cancel your app access.
If you want to provide a way for the user to logout from your app, you can do it on your login implementation (if you have a backend, of course), otherwise just send the user back to the login screen and delete the token.