I recently updated to google chrome 23 and sound stopped working again in flash player.
its because of the bug in chrome 23. To fix it follow these steps.
Click on the Windows Start button > Control Panel > Sound > select the speaker/playback device and click the Configure button > in theSpeaker Setup dialog that appears, if you have multiple audio channels listed, please test the Stereo configuration, and let us know what happens. select stereo option if any other option selected.
More details here.
update : Still no permanent solution from Google and the sound quality also not good in chrome. So I installed IE Tab, a google chrome extension which helps me to open the flash player sites in chrome itself (with out opening internet explorer) and no need to change the sound settings.
update2: Still no solution from google. I uninstalled latest version of google chrome and installed the old version(22) from here in which flash sound is working fine. Never go to about google chrome in the menu, otherwise it will update it to the latest version of google chrme.