Screensharing with the Flash Media Server (FMS) has been reserved for use by Adobe for some time. They have made the business decision that they want to keep it close to the vest. This has all become increasingly annoying over the years and thankfully some great developers have stepped up to offer this functionality to the masses.
JScrCap is a java application that allows you to stream your desktop to a Flash Media Server. This includes Wowza as well as FMS. There are some gotchas to both but I'll let Vivek explain them a bit more. He has a write up here: http://viveklakhanpal.wordpress.com/2009/07/23/jscrcap-screen-capture-utility-for-both-fms-and-wowza-media-server/
This is a great step forward and I look forward to using it as a replacement for the current desktop share that we use now in Huddle.
UPDATE: As of Flash Media Server 3.5.3 you can now stream directly to FMS with a 3rd party screensharing application.