900: I think it's mostly accidental. When you work with gas in such a hot environment, anything oily will catch fire quickly. I guess it might help you go a bit faster in some cases but unless you are flambéing, it probably shouldn't be intentional.
Most of the time it is not intentional, then there are times that it is intentional. For example; if I need to make a sauce a la minute on the fly, I will get a pan hot and add (Kids don't do this at home )alcohol and flame the pan to burn off the alcohol. Then finish the sauce.
It depends what you are cooking. Every food item has a different 'smoke' point if you will. As you know, searing a portion size piece of meat over high heat is better than cooking at low heat because caramelized meat tastes better than boiled meat. Flames in this case might help a tiny bit. If you want to bring out the sugars then high heat is important but maybe not throughout the entire cooking process. That said, I can't think of a single sauce or stew or soup that tastes better cooked over high heat. Sometimes slower is better.
I think that the flames are mostly unintentional. As mentioned before, fats or alcohol added to a hot pan will sizzle and spit over the edge of the pan, catching alight very easily.
That said, it is something that you don't want to happen if you are sauteing or shallow frying because flamed oil gives the food in the pan an awful, acrid and slightly metallic flavour.
Anyone who makes flames just to impress the diners isn't really looking after their food.
But hey, it is kinda fun.
Apparently, the flames ignite the unburnt gas over the pan and the flavour that results is from the odour in the gas burning off. Yucky if not intentional and impossible to get rid off but if intentional (i.e.) flaming a wok, sometimes adds to the flavour.(i think)