I’ve done some exploratory research on the feasibility of wrapping Mullvad into a Flatpak and I don’t think it’s possible at this time.
The fact that it requires host network access is the least of our problems, as it should be easy to give the sandbox access to the host network namespace.
The big issue instead is that the desktop application relies on a system-level daemon that can either be configured to start at boot, or the application manages itself when you start or stop the VPN. The GUI is just a shell that talks with this daemon via RPC: mullvadvpn-app/architecture.md at master · mullvad/mullvadvpn-app · GitHub
With flatpak there is no way of running background daemons, which would break the “start VPN at boot” option, and the fact that Mullvad expects to interact with this daemon through systemctl, which isn’t available inside the sandbox, pretty much makes it impossible to be packaged as it is, without major changes upstream.
Sadly, Mullvad has said many times they do not have the bandwidth to explore alternative configurations than the standard .deb and .rpm they provide so unless someone has the patience of rearchitecturing their application and getting it approved and merged in the first place, there’s not much we can do.