Don't believe me? Just take a look at the many popular flash based services that are moving away from the stale technology. Two such examples of this are the music streaming service Pandora (which is now fully HTML5) and the popular video streaming site Youtube (which currently offers a beta HTML5 version). Google+ also display any linked to Youtube videos using the HTML5 technology.
It isn't just websites that are predicting the end of flash though. Microsoft recently announced that it's new version of Internet Explorer for Windows 8 on ARM will not support plugins of any sort. In fact they went so far to state the obvious: