The draw Hickock used is discussed as the "Cavalry Draw" in Chic Gaylord's book, Handgunner's Guide.
"The cavalry draw as used by John Wesley Hardin, Wild Bill Hickok and Doc Holliday, is the fastest known method of drawing and firing a single- action. It is the rarest of draws today because so few will take the time to master it. It takes longer to show results than with the more conventional tied-down holster draw. This draw requires a scabbard held high with an extreme forward tilt. The revolver is held with the bttt reversed and is wrn just behind the right hip. The draw is begun by raising the elbow almost ot shoulder heightm then slammiing the hand back onto the reversed gun butt with the thumb across the hammer. The gun is then thrown forward out of the holster as the elbow is snapped down to the side. This whips the gun around into the firing position. The weight of the gun against the thumb cocks the gun with no conscious effort on the shooter's part. All that is left for you to do is fire. The gun should be fired the instant it is on target."
I tried this years ago, with an unloaded gun, and it does work. I stopped fooling with it, however, because I almost always pointed the gun at some part of myself as it came out of the holster. A word to the wise should be sufficient, eh?
Hangunner's Guide was reissued a while ago. It may still be available from Paladin Press.