How to configure an isolated Artifactory Docker container environment?

An appropriate approach for setting up an Artifactory High-Availability setup with containers isolation would be to using multi-host networking (Available on Docker 1.9+).

Docker Swarm is optional, but not required to configure multi-host networking. A good tutorial on this is available on Docker GitHub’s page. After setting up a Key-Value controller, you could add an overlaying network for your Artifactory HA nodes. On top of that, you could add an additional, e.g. Nginx, server to the already built network to allow load balance, and to serve as an exposed (only) endpoint to the underlying HA setup.

Overall, through Docker multi-host Docker networking, and without exposing any dedicated ports you will establish an isolated environment for your Artifactory.