I don;t know of any rule that states the style of 'flick' to be used, as long as it is your finger, except in cues play, where a cue stick is used.
I know Bryan Cook deploys this style when shooting open 20s. On tournament quality boards, you don't need a massive amount of power, so I'd say its a matter of finding the method that works best for you. Like Clare said, as long as you use a finger (I've seen a lady shoot with her thumb!) it's wide open. Personally, I shoot with the right index finger braced by the thumb.
Exactly. whatever works best for you, as for me it is my left index finger. Although sometimes even that doesn't work well (: Lately I have been practicing with my right index finger, but that still needs a lot of work !!!