Hi,
They are compatible in the sense that they can be used to navigate while flying MSFS on an Xbox, using our Charts apps that run on e.g. iPad or Android. They match the built in navdata quite well.
It isn’t possible (at least currently) to load Navigraph navdata on Xbox, nor use the moving maps functionality to track your position on the charts. More on that in this thread: Native Xbox Series X MSFS moving maps support?
Regards,
Stephen