How do I use Bluetooth or Airplay with TuneIn?

Open the TuneIn app, and play your desired station or podcast. In the Now Playing screen you will see Chromecast and AirPlay buttons under the station's logo or "Now Playing" artwork. Tap the AirPlay button to select an AirPlay-enabled device you would like to listen from. 

You can also do this from your iOS device's Control Center. Once playing the desired station, just swipe up from the bottom of the screen. That should open up the Control Center on your iOS device. From there, you can select a Bluetooth or Airplay-enabled device to listen from.