I guess you could take exactly that
picture, make it the size of your screen, load it as a flixel sprite and
put it over everything you have.
Then give it a scrollfactor of 0 so it always stays in the view.
If UI should not be affected by it, you can add that layer so that it will appear over this effect graphic.
Does that work for you?
var effect:FlxSprite = new FlxSprite(0, 0);
effect.loadGraphic("assets/images/box-shadow.png");
this.add(effect);
effect.scrollFactor.x = 0;
effect.scrollFactor.y = 0;
I've added it to my game as a try:
Is that what you need?