After much troubleshooting, I figured out how to get this app to work.
The trick is your iphone has to be set up to sync over WIFI with itunes. Verify this. Try syncing it a few times. The app should work then. Sometimes you still need to restart the app on your iphone or try connecting to dragon a few times but generally it will connect 80%+ of the time on the first try as long as your iphone is set up to sync over wifi.
aicccia about Dragon Remote Microphone