1. Set up VoiceOver
Firstly, go to
Settings > General > Accessibility > Accessibility Shortcut
and check VoiceOver
2. Start a broadcast
Now start a Periscope broadcast as you normally do. Once you have set the orientation triple-click the Home Button. Tap once where the comments usually appear on the screen. All comments should now be read aloud as they appear.
3. To stop a broadcast
When you want a broadcast, stop VoiceOver by triple-clicking the Home Button. Then exit as you normally do.
Bonus – To tweak VoiceOver
You can change the voice and speed of the VoiceOver in
Settings > General > Accessibility > VoiceOver