Is there an API to get a list of all Custom Object classes?

There is no standard API for getting a list of all classes. However, you can create an alternative, e.g. create a 'MyClass' class and store all classes in it.

You can find more information how to create a class here:

Server API -  Custom Objects
SDKs - Custom Objects | SDK | QuickBlox

Feel free to check out official documentation for more information that will help you to integrate QuickBlox services into your applications / projects or contact our Support team by submitting a ticket if you have any other questions.