Little bit of code to show how Flash doesn't handle a redirect, which is incredibly common for interacting with Facebook images.

RedirectTest

package
{
    import flash.display.Loader;
	import flash.display.LoaderInfo;
	import flash.display.Sprite;
	import flash.events.Event;
	import flash.net.URLRequest;
	import flash.system.LoaderContext;
	
	public class RedirectTest extends Sprite
	{
		public function RedirectTest()
		{
			var l:Loader = new Loader();
			l.contentLoaderInfo.addEventListener(Event.COMPLETE, onComplete);
			l.load( new URLRequest('https://graph.facebook.com/4/picture'), new LoaderContext(true) );
		}
		
		protected function onComplete(event:Event):void
		{
			this.addChild((event.target as LoaderInfo).content);
		}
	}
}