Flatpak is just a cheap container copy. Can't do anything beyond what cgroups and things like apparmor and selinux can do, and uses a runtime to do soft higher-level policy functions that translate down to the same primitives. If anything, it's a great bundler, but doesn't do anything new policy-wise.
So, can you get the macOS-level capabilities (both low-level and higher abstractions)? On Linux, yes, but they don't exist yet. On Windows: technically possible, but since that would break most GUI workflow it's not likely that anyone is going to bother, and you're going to have a hard time recompiling windows yourself to make that happen.
On macos i currently virtualize the process itself, but this has virtualization overhead and some emulation overhead because macos does not let you map all the host process pages to a guest.
You can use Linux's sandboxing functionality to make a pretty hardened server. If you take in mind the physical deployment and go the extra mile, it can be very secure. The Linux desktop is not and will never be secure in its current form from things like extremely basic local malware. You would have to redesign much of the desktop stack from the init system downward so you could easily do things signature-based identity, proper per-identity secure storage and key management, securitizing elevation of privileges, getting rid of setuid, etc.