There are currently no tutorial-style instructions for using anything but Vagrant, but you should be able to just to run these commands in whatever environment you are using: https://github.com/flynn/flynn-demo/blob/26fcd98cd7646199513...
In the meantime, you should either a) install the latest docker from the official docker APT repos http://docs.docker.io/installation/ or b) do something like ln /usr/bin/docker{.io,}
In any case, don't leave your Docker install without a docker binary in your path. That will universally break all tutorials and scripts ever written for Docker, and is unsupported by us (Docker maintainers).