Is there an app for iPhone to record the audio output streaming of any other app ?
This link shows the steps on mac. https://www.apptamin.com/blog/capture-iphone-ipad-screen-video/

You use Quicktime, 
Connect your iPhone or iPad to your Mac via the lightning cable.
Open QuickTime player.
Click File then select 'New Audio Recording'
A recording window will appear.
Select the Mic of your iPhone if you want to record music/sound effects.
Click the Record button.
You will not hear the sound, but the levels show the input.