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 (Google / TripIt / any email via IMAP option) 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.