AirPlay video with audio on iOS device
That is currently not possible.

You can make it a feature request to Apple

here

http://www.apple.com/feedback/appletv.html

or here

http://www.apple.com/feedback/iphone.html

You can come up with your description but here is a draft:

*


  Feature request: I'd love it you could activate "private listening"
  with Apple TV. Pop headphones into your iPhone or iPad and listen to
  the audio from the Apple TV it's connected to without bothering other
  people in your living space.


*