Possible to record audio output streaming from other apps?
I don't know of anything on the phone itself but getting audio out of an iphone and onto something that can record is possible.

Using AirPlay and Airfoil Satellite (or your Airplay receiver of choice) you can get the audio to your Mac. Then using Audio Hijack (as mentioned by Kalamalka Kid) on your Mac you can record it. 

Not the most ideal setup but it works.