Yes! BookBeat for Android has Chromecast support for app version 8.6 and later and on iOS you can use Chromecast if you have at least app version 9.14.
On Android:
If a Chromecast is available, you will see the Chromecast symbol on the book page and in the audio player and you can cast to your device.
On iOS:
Press the loudspeaker icon on the lower left in the audio player to get to the "Google Cast" tab.