All apps installed through Flathub display a black square instead of the camera. Apps not installed through Flathub can still use the camera.
It would help to have a few more details, such as the apps you’re experiencing the issues with, and the desktop and distribution you’re using.
But, as a general hint, Flatpak apps need to access certain system resources, like the camera, over a desktop portal. In the case of the camera, this would be the Camera portal.
So the first thing I would check is if the portal implementation for your desktop is properly installed and enabled.