The “device registration API” code (3. Toward the bottom of the page) looks like Javascript (same as on the “SDK for JS” page and in the video). A quick look at the Flutter Backendless code shows:
should be messaging, not Messaging,
‘registerDevice’ needs a list parameter with three elements,
there’s no ‘AsyncCallback’ method,
looks like there’s a single ‘_handleMethod’ method, not separate ‘handleResponse’ and ‘handleFault’ methods
Can’t say if the Flutter API documentation for device registration for push notification is up-to-date, so will leave this topic to be marked ‘solved’ by support staff.