When connecting a webcam class to a Video the Privacy settings automaticly appear.
video.attachCamera( camera ); 

But if the user clicks DENY instead of ALLOW you can get into a little problem. My application needs a webcam so what I do is to show the user some copy and telling them to ALLOW the webcam or go somewhere else to play.

To check if the first time was allowed or not is easy with 
camera.addEventListener(StatusEvent.STATUS, onCameraStatus);
but this is only triggered first time, event if I create a new Camera and Video class. 

Solution
After the first event I set a variable that the user has already got the Privacy window. IF the user selects DENY and I want to give them another change (after my nice warning window) I do everything EXACTLY the same way, JUST ADD
Security.showSettings(SecurityPanel.PRIVACY);
If it’s the next try.