How can I log out (or sign in) to the app?

In the App in the Air, we do not have a standard account definition for logging in and out. 

You can optionally use different log-in methods (Facebook, iCloud, Google, Outlook, Apple) to import flights. You can then use such "login" methods to sync flight data and subscriptions between devices (iOS / Android).

However, you can disable any connected account. Just go to the app settings and click on it, then confirm.