You can only use it in Rock Tunnel, where it's really dark and you can't see a thing :p
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When a Pokemon has the move Flash, you go into Party, then select the Pokemon with Flash using the 'A' button and there should be an option that says "Flash". It is only usable in dark locations or within battle.
No that would be nice though to get more light defeat pokemon.
Go to the top of Sprout Tower in Violet City and battle the guy who your enemy guy just battled. When you beat him he will give you HM Flash.
To my knowledge i don't think there is a waterfall in Pokemon yellow and it is quite irrelevant to the storline if there was one. If you mean a HM named waterfall...i think your on the wrong game, only pearl and diamond have waterfall HM...i think. There are only 5 HM's in Pokemon Yellow Flash, Cut, Fly, Surf, Strength.
In Pokemon Platinum, Flash is a TM.