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.
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.
Press the loudspeaker icon on the lower left in the audio player to get to the "Google Cast" tab.
Please observe that this feature is not available if you have a Huawei device without Google Play services.