Recently (July 2015) we discovered Flash was no longer working on the Steam browser engine. Previously we installed ‘Flash for Other Browsers’ (e.g. Firefox). This was an NPAPI version of Flash Player which worked perfectly fine, but is becoming deprecated.
The preferred version of Flash Player is becoming the PPAPI version. If you download and install the PPAPI version of Flash Player, then restart Steam, you should find Flash fully works on the Steam browser again.
Lack of flash ads
As a result of Valve’s changes we are seeing a lot more HTML5 ads being served versus Flash. This has affected some geos negatively, however, we prefer working with HTML5 as we find it more responsive and less likely to crash than Flash.