I just found that turning on custom vibrations in accessibility options made the LED flash alert work in my 4S. I had been trying to get it to work again after having tested it when I first got my phone. The feature must have been switched off during subsequent restores (due to buggy iOS installs).
Furthermore, I've tested the LED alert flash with the camera flash turned off for both video and still cameras. It works fine irrespective of the camera flash settings.
I don't think it makes much sense that you have to turn on custom vibrations in order for the LED flash alert to work. There's no indication anywhere that one is dependent on the other.
Now I can say I have a 'flashy phone' 🙂