I wish it would be possible now but it probably won’t happen until windows and mac will have similar features. The problem is that processes cannot just read a file, because in the container it doesn’t exist. It’s maybe due to permission. Maybe not. You cannot tell. Android apps are written in a way that they request access, while pc apps are just reading the files directly without requesting permission.
So the app has to be written for flatpak. However, afaik, this is the maintainers goal too. Btw, the file open dialog is a currently working example of the dynamic permission handling. It’s just that the app should use these features which is not guaranteed.