This dialog appears the first time you save an entry with the facbook checkmark ticked.
The first thing you should do is to login. Press the "Login" button to login. Login screen
Once logged in, Flight Journal will remember your account until you log out (also in this dialog).
Now that you are logged in, you can type a message and press share - your facebook wall will then be updated.
Always use facebook sharing? Simply tick "Remember choice". Remember..