Flash Player Update
I've tried several solutions to the lack of Flash Player support in Chromium OS, and all the solutions that Google turned up haven't worked. So it looks like if you want to use Chromium OS you'll have to live with no Music playback including from Google Play Music, no Video playback including Google Play Movies and TV and partial YouTube playback.
I suppose this is the only drawback of using Chromium OS as it doesn't have the same level of support that Google puts into Chrome OS as relying on a third-party to compile a generic build of Chromium OS is asking too much. The version of Chromium OS that I'm using hasn't been updated by the dev Hexxeh since he put up Build 4028 on the 20th of April 2013, so I'm not holding my breath at a newer version or even a way to get Flash working.
I've asked Hexxeh on via his Google + Profile if he's going to bring out a new build or if it's possible to get Flash working, but I'm not holding my breath for a reply.