Bookly is compatible with the vast majority of WordPress themes and, as long as the theme is developed according to the Wordpress Codex, it is most likely compatible with yours.
While it isn't technically possible for us to test all themes out there, incompatibility issues have been rather rare in our experience.
In order to make sure that your theme works with Bookly, your best bet is to try installing the free version of Bookly plugin. If the free version works with the theme, then the Bookly PRO version will as well.
And we'll be happy to help should you encounter any compatibility problems. Just email us at support@bookly.info.