On Linux I encountered this for a while with a couple of Flash versions and had to use a older version of Flash until Twitch fixed the issue after I reported it.

Try making sure Flash is set to always activate when viewing Twitch and you may have to refresh the page until stream loads.

There is a alternative that may work for streams but with no chat. Replace end of link with channel name. The newer player still has Flash embedded.

The newer player can be viewed at http://player.twitch.tv/?channel=insertchannelnamehere

Twitch is looking to use HTML5 for video as they have already switched to HTML5 for chat and the controls on regular player.

Also Hulu doesn't work either. and the new twitch player doesn't load either.