I've followed the Adobe instrunctions on how to create an app without windows (link).
The gist is that you can do this by hiding or closing the original nativeWindow and creating a new one with theUTILITY or LIGHTWEIGHT property.
Unfortunately, when an application is launched more than once, the new nativeWindow is created again with each launch. This is highly undesirable. Anyone out there who knows how to prevent that from happening?
I've tried setting variables with the launch of the application, but it seems like these are not accessible by the new instances of the application. The weird thing is: AIR apps are not supposed to have multiple intances (should be impossible)! And there actually is only one instance according to the windows task manager and the fact that there is only one systemtray icon.
I'm making the application with Flash/AS3, I don't know yet how to use FlashBuilder/Flex.
I how hope so much that you have a solution!