A simple search of this forum or in google would have pointed to numerous identical queries and the answer.
You don't need Flash as YouTube these days uses html5 instead. You need the latest official YouTube app from Google Play. Use it instead of the pre-installed unofficial app that Archos supply (which used to work but is now useless). To watch YouTube videos while in the web browser you need the official YouTube app and to browse with Opera Mini browser.
A little more info at http://forum.archosfans.com/viewtopic.php?f=74&t=66978#p405862