Hi Dave,
I'm aware of what kernel configuration changes is required, and how to build docker for chromium OS. In fact, it is going to be included in the next release of our Chromium OS based OS, Flint OS. I've been running it on my test system for a couple of weeks and it runs great.
I'm understand that you would like to keep the original Chrome OS as is as much as possible. That probably is doable but different from my approach. I'm still listing what I did as below, just for your reference.
First, follow the Chromium OS developer guide to setup local Chromium OS build environment. Once that is done, find out the board name of the Chromebook from /etc/lsb-release and setup board, build package, build image for it.
Then port ebuilds of docker and its dependencies from Gentoo portage tree to the board, and build docker. There are a few patches required to make docker and runc package compatible with how cgroup fs is mounted in Chromium OS. I also created docker upstart script to start the docker daemon on startup, with some required pre-start operations.
Finally a Chromium OS image can be built, with the kernel that support docker and the docker program itself included. Install it on the Chromebook and it's done.
There are many commands to run and many problems to solve. If you are a experienced Linux user you will find it is a bit complex but not too hard to work with. If you have questions, just ask here and I'm sure many people will be glad to help.