Is there a way to export the flight movie complete with the stick movements and overlaid data. I would find it very useful to keep but apart from playing on the iPhone, I cannot figure out a way to save it?
Not possible. You can turn on subtitles and you'll get very basic telemetry when played in something that can read .srt files. Other than that, you'd have to export the .txt log files into an online converter and use something like Dashware. But no stick movements.
There are quite a few screen recorder apps for the iPhone. I use reflector on a macbook air that sits in the boot of the car. Very handy to analyse what happens after an event - I had occasion to use it with a PV+ that ditched into a reservoir last April! For recording stick movements, you could attach a GoPro to the controller and synch everything up together to get full analysis.