You can dispatch asynchronous events back to your actionscript application by using the dispatchStatusEventAsync function of the FREContext class. You'll need to store a reference to your FRE context somewhere and then call the function as below:
yourFREContext.dispatchStatusEventAsync( "anEventType", "some data" );
This will dispatch a status event to your actionscript context which you should add a listener to when you create your context on the actionscript side of your extension:
yourExtContext = ExtensionContext.createExtensionContext( "your.extension.id", null );
yourExtContext.addEventListener( StatusEvent.STATUS, extension_statusHandler, false, 0, true );
Then in your listener:
private function extension_statusHandler( event:StatusEvent ):void
{
trace( event.code + "::" + event.level );
// should trace from the above: anEventType::some data
}