Cromium doesn’t seem to be offically supported anymore:
Installed flash-plugin.x86_64 0:22.214.171.1248-0.1.el6.rf just before.
In order to get flash-based content playback working,
One has to use the currently supported NPAPI instead of the obsoleted PPAPI.
The Adobe plugin needs to be enabled, Pepperflash disabled – then it works
(well, removing Pepperflash might have the same result):