Is it possible to trigger click event on Flash object via JavaScript?
It is possible with Flash ExternalInterface, but you need to write some ActionScript in Flash (.fla) first.
Some references -
Using ExternalInterface in Flash
http://www.actionscript.org/resources/articles/638/1/Basics-of-using-the-ExternalInterface/Page1.html
http://www.adobe.com/devnet/flash/articles/external_interface.html