I have not tested it, but i have a feeling that trying to crowbar in an AirPlay solution is going to be more trouble than you think. For AirPlay (or Reflector) to work, the phone needs to be on the same wifi network as the AirPlay destination device. You can probably do that by joining the phantom network as the post above describes, but I wouldn't count on it not interfering as the user claims above. So that probably kills it right there. Vision+ FPV is transmitted via wifi, so you need the phone to be on the Phantom network. Any of your AirPlay destination devices (ie Apple TV) will not (or should not) be on the same network and won't be available to the phone.
That's why I said above, your best bet is probably going to pull the video feed out of the phone (using an HDMI or DVI adapter) - just like you do to connect FPV goggles, and send the video to any number of commercially available video transmitters (wifi or analog radio), to broadcast to your other devices.
A video transmitter should be pretty cheap too, especially since you don't need HD. Actually, you would probably do something like this. IPhone -> Apple VGA Adapter -> VGA to RCA converter -> generic SD video transmitter -> TV, monitor or whatever you connect a video receiver to.
The more expensive (but less crap to connect) approach would be: iPhone -> Apple Digital AV adapter (ie HDMI) -> HD video transmitter -> TV, etc
