Finally, found a way to display system notifications for AIR applications! I’m using as3notificationlib for doing it. From the library’s Google Code page:
This project makes it easy to add cross-platform notifications to your AIR application. It handles “native system notifications” like the dock icon bouncing and the taskbar icon flashing, and it allows you to easily create alert “pop-ups”.
In addition to displaying text in the alert “pop-ups”, one can also add an icon, a video and a sound alert (to indicate display of the “pop-up”).