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

At App in the Air, we don't have a standard definition of the account to log in and log out. 

You can optionally use different login ways (Facebook, iCloud, Google, Outlook, Apple) to import flights. You can use later on such ways of "login" to sync your flight data and subscription across devices (iOS / Android).

However, you can disconnect any account you connected. Just go to the app's settings and tap on it, then confirm.