I'm thinking this is a matter of state law. I don't believe "dive boats" have to display a flag unless they are engaged in diving at the time. And if the individual diver carries a flag, that is probably sufficient legally, whether the boat has a flag or not (under the federal COLREGS, the only flag required of a dive vessel is the blue/white "A" flag, plus restricted maneuvering lights at night if not anchored). Helpful hints here:
http://scuba.about.com/od/divemedicinesafety/tp/Dive-Flags.htm
But let's talk practicalities. The flag on the boat, whether Alpha or red/white, is higher up, and easier to spot. And if you get far away from the boat, then having your own flag, while a pain in the neck (arm?) is a good idea, and probably required anyway once you get outside the flag-radius of the boat that other traffic must avoid (varies 50-300 feet according to the link above). And the dive flag on the boat does indicate to the distant observer what's going on, and that the boat is probably (or legally, if the Alpha flag is up) not able to maneuver freely.
All this, of course, assumes that other traffic understands what the flags and lights mean. Most do, but definitely not all. So more is better, which is why you'll see large painted dive flags on hulls plus a flag on the mast, plus the Alpha flag. The more the merrier (we hope).
Not the best area to adopt a "minimalist" approach, even if legal.