I'm not entirely sure what caused that dude's death, but drinking a bunch of redbull probably isn't the way to go. Death by caffeine is probably super painful and uncomfortable.
If you're really motivated to go that way, though, then buy caffeine pills or powder (I'd recommend pills since the powder tastes like shit) so you can quickly get to a lethal dose. In caffeine overdose cases that I've seen, I think people used like 10 grams.