FlxCamera contains a built-in FlxCamera.flash() function which will fill the whole camera with a solid color that fades out over some time.

// flash the screen red, and have it fade after 1 second
FlxG.camera.flash(FlxColor.RED, 1);

Demonstration

package;

import flixel.FlxG;
import flixel.FlxState;
import flixel.util.FlxColor;

class PlayState extends FlxState
{
	var timer:Float = 2;

	override public function create()
	{
		bgColor = 0;

super.create();
	}

	override public function update(elapsed:Float)
	{
		timer -= elapsed;
		if (timer <= 0)
		{
			timer = 2;
			FlxG.camera.flash(FlxColor.fromHSB(FlxG.random.int(0, 360), 1, 1));
		}

		super.update(elapsed);
	}
}