I recently discovered a way to play voice memos in the background on my iPhone. Why they don't display this behavior by default is baffling to say the least.
There are several published hacks to do this, and most of them involve sharing the memo with yourself via Messages.
My method is somewhat similar to this one1 and involves the least amount of intrusion.
- Open Voice memos and play the memo.
- Lock the screen.
- Wake the phone using the power button.
- Slide up to go into the Camera app.
- Press the home button to return to home screen and you will notice that the memo is playing in the background.
If you have your own method that works for you, but involves more steps, you can add this one to your list. I tested this on iOS 8.1.1 (12B435)