Flamenco, the official render farm for Blender maintained by the Blender Foundation currently has no Docker support, and from discussions with the primary maintainer, it sounds like the Blender Foundation doesn’t have the resources to build, maintain, and support a Docker image for Flamenco.
Flamenco is comprised of the Manager and the Worker, with tar.gz packages hosted at https://flamenco.blender.org/.
The Manager would probably be simplest to containerize initially since it’s just a static Go binary and a custom binary of ffmpeg, along with a YAML config file. The Manager does currently look for Blender during startup, but that can be disabled in the configuration: #100195 - Allow finishing setup assistant without Blender on Manager - flamenco - Blender Projects.
The Worker requires Blender, so would likely be built from the existing Blender image, and may be more involved, especially to elegantly support Blender add-ons that users will require for render jobs, although that’s probably more of a concern of the Blender container itself. I will say that I personally am mainly interested in running the Manager on my home server in a container, but will not be running the Worker in a container for now since that will be running on Windows workstations until I have the funds for dedicated GPU servers.