When placed correctly (ie the noseband is 1-2 fingers below the cheekbone with space for at least 2 fingers under the cavesson and even more under the flash) a flash serves to keep the snaffles bit quieter in the horses mouth. It will not and was not ever designed to stop the horses jaw from crossing, like a figure 8. The flash is most commonly seen with loose ring bits as they are the most noisey in the horses mouth. Egg butts, dees, etc are all quieter and that is why they are favoured in hunters where flashes are not allowed.
Drop nosebands are similar in function to a flash. I find the flash better for most horses as it transitions well into a plain cavesson used with a double bridle. Flashes and drop nosebands should not be combined with any leverage bit or gag, where as figure 8s and grackles can be used with these bits.
Eta the picture in that article features an atrocious adjustment of a flash which is not the fault of the equipment, but of the person putting it on the horse. Posted via Mobile Device
I hate flash nosebands and would personally burn anyone who tried to stick one on my horse - who for the record goes in a correctly adjusted drop noseband meant to guard purely against excessive gaping because he's green and doesn't need to learn that habit.
The problem with a flash is that when you adjust them correctly, with two fingers under both straps, when the horse gapes he's going to pull down on the flash portion, which moves the junction between the two straps down the nose making it a useless strap floating around your horse's mouth. This is why people who use them will tighten them right up on both straps, to prevent the movement, which actually makes it move just as much because there's more pressure pulling it all down than there is keeping it up (which is what's happening in the photo from the article above). Don't believe me? Find something cone shaped and try to tie a piece of string around it - it will ALWAYS move towards the narrow point as you tighten it.
As for the flash vs drop argument - it's mainly fashion that fuels the fight there. The common opinion is that drops make heads look long, and this is true to a certain extent. Drops don't suit every head, BUT would you rather a pretty looking noseband or a functional one? I know what I prefer.