It is possible, but if you are confused as to how to get an X server _installed_ (much less running) on CoreOS, I urge you to reconsider your choices. In particular, examine why you want to run a GUI on a server OS. What is it that draws you to CoreOS/ContainerLinux? You appear to not already be aware of the container-oriented nature of it, which makes the choice less sure.
Common prototypical reasons (and alternative thought) for being drawn to Container Linux _other_ than for its server role:
- Automatic updates: these are often available from desktop OSs with add-on software and/or add-on services
- Highly-compartmentalized (container-oriented): consider Qubes OS[1], virtual machines, or even containers _on_ a desktop OS
- Small footprint: consider a more customizable OS, such as Gentoo or Arch, such that you can install just the pieces you want
- Builds/installs from a spec (declarative install): consider NixOS[2]
Assuming none of this has thus far dissuaded you:
Like any other piece of software in CoreOS, you would "install" an X server by creating and pulling a container image. You are perfectly free to include whatever random software you want to include within your container, and you can even use package managers to do it. Just take a look at almost any Dockerfile out there, up to and including the Docker-official images.
_Running_ the X server is the harder part. X generally requires (at a minimum) root access and device access, and an untold set of other requirements not generally available within a container.
Jessie Frazelle[3] has done a lot of work in the area of running GUI applications inside containers in the past, so you should definitely take a look at her materials, but know that this is definitely _not_ a goal of any of these components.