This is a feature that is exclusive to Adobe Connect - and isn't supported in the current Flash player or Flash frameworks (Flex/AIR) outside Connect.
However, realizing this kind of feature is possible with Merapi http://www.merapiproject.net/ - using Java to do the screen capture and mouse movement. If you are looking for cut-and-paste code for a solution... I'm certain you're out of luck. There are some good libraries out there though that are worth looking at. For screen capture there is JxCapture http://www.teamdev.com/jxcapture/index.jsf mouse control can be easily accomplished with native OS calls using their JNIWrapper.
If you are interested in a really low-res solution. Install VNC server on the machines you want to communicate with and use Flash VNC.
A word of caution - this kind of solution isn't something that you want running in the sys tray or dock. Screen capture and mouse control present significant security risk...
ScreenCamera SDK is definitily your best option here. It installs a camera on the system just like a regular webcam to which you can connect using Flex. ScreenCamera SDK remains completely invisibe to the end user so it looks like your app is doing all the video capture and recording and sharing.
You can test it from here:
I think this is the simplest more practical way to do what you want to do,