If it seems that your iPhone is not recording the flights it could be that you have prevented the SeeYou Recorder app to use the location services on your iPhone. The location services are required for SeeYou Recorder because this is where the GPS position comes from.
To enable SeeYou Recorder to use the location services please open the Settings app on your iPhone or iPad. Then go to "Settings->Privacy->Location". Make sure that the "Location Services" for "Recorder" are turned on as shown in the following screenshot: