It seems there's no good enough up to date open source Flash player project. And apparently current Lightspark won't work with Chromium version 34 and higher.
Starting from version 34 (April 2014) Chromium/Chrome start to drop support for the Netscape-API plugins (NPAPI) in favor to new Pepper API (PPAPI) which runs plugins in sandbox mode (which, IMHO, closed the main web security hole of the last years named Flash). To keep Flash support under Linux Google made deal with Adobe to maintain its own version of Flash (still proprietary and close sourced) available as
Since the latest version of Lightspark was long before (2013-03-16) the API switch (2014-02-17) it doesn't supported by current version of Chromium project. The other active FOSS Flash player projects are even older.
What to do
Depends on reasons you're seeking FOSS Flash player.
In case of security, you could safely use Google's Pepper Flash, since it's sandboxed. Install it via Ubuntu Software Center as
pepperflashplugin-nonfree or command line
sudo apt-get install pepperflashplugin-nonfree. Chrome already includes plugin build-in.
In case you believe in FOSS software and want to support it - it's better to not use Flash at all (ignore it), as using any FOSS players still promote closed proprietary RIA standard (which, IMHO, harmed industry enough). It's not so hard, since many sites going to use HTML5 as Flash replacement. And as backup feature you can install Pepper Flash, but set Chromium to run it only by request (entering URL
chrome://settings/content and selecting "Click to play" for Plug-ins).