I'm not entirely sure if it is important to you to used that specific flavor of chromium or if you are simply asking how to solve the flash crisis.
After much frustration and hunting for answers for how to make either firefox or chromium operate flash under Ubuntu, my solution wound up being slightly better than defeat. I discovered a few weeks ago that Google's Chromium browser for Ubuntu actually displays flash properly.
By default, the Ubuntu Software Center does not offer that program, but it seems there's an easier way than editing software sources. I discovered that if you download the correct linux version from the page at the following link, it adds this software source to the sources list of the Ubuntu Software Center and proceeds to open the center and to install that browser.
I have a few opinions about how the Ubuntu Google Chromium browser operates slightly differently from Chrome, but they could just be impressions. I seem to get more breakthrough audio from ads on tabs other than the one I'm looking at, but as I recall that was a problem with Chrome as well.
Here's the link I mentioned:
https://www.google.com/chrome/browser/#brand=CHMB&utm_campaign=en&utm_source=en-ha-na-us-sk&utm_medium=ha
PS: My sincerest apologies if you were specifically seeking advice to make that particular variant of the chrome browser work with flash. By all I've read to date, nobody has solved its problem yet.