Distrobox, by default, doesn’t provide much isolation/sandboxing - it’s main aim is desktop integration and filesystem transparency. So if you’re trying to use it for isolation, it’s a bad idea.
However, you can create a new container which will isolate your filesystem and prevent such conflicts, using the –unshare-devsys flag. (if you want FULL isolation though, use the –unshare-all flag).
Then enter the container and install the flatpak app as usual.
I just tested this on Fedora uBlue and an Arch container and it works fine, didn’t have to unmount anything.