Note: This functionality is currently available in the Android app only. It will be added to our iOS app in the near future.
Make sure your Libro.fm app is updated to the latest version (Android app version 7.28 or higher).
Select your audiobook from the Library screen and tap Play to start listening. Then, tap the Casting icon at the top right-hand side of the screen.
The icon you're looking for is indicated by the arrow in the image below: