I don't think Docker is comparable to bubble wrap. The latter is a lot more flexible. Docker is a pain with GUIs, and difficult to have a customizable way to "break" isolation when you need to, like having applications talk to each other or exchange files, etc.

But Flatpak has its fancy "portals" to connect each app with the specific resource it needs which you don't get with Docker.

Also if the goal is to limit access of apps you don't want to fully trust, I think Docker doesn't have the appropriate security properties. Here's a quote from the readme for Bubblewrap (the sandboxing tool that Flatpak and Nixpak use),

Many container runtime tools like systemd-nspawn, docker, etc. focus on providing infrastructure for system administrators and orchestration tools (e.g. Kubernetes) to run containers.

These tools are not suitable to give to unprivileged users, because it is trivial to turn such access into a fully privileged root shell on the host.