While I respect that you want more apps you use into the same package manager. I may be wrong, but its my understanding that they dont accept docker containers on flathub. I don’t even know it is possible to run docker inside a flatpak or if its possible if it would conflict with docker on the host. Docker or podman requires kernel features like cgroup which I belive flatpak sandboxes away.

At the very least you need docker or podman and kvm and pass these from the host into the flatpak

I really like having all or most apps in one or max two package managers on my computer. But I think this is a case where you might have to concede installing this piece of software without a flatpak