Octopuses do expel ink from their siphons, which are also the openings through which they shoot water (for swimming) and bodily waste. So although not exactly flatulence, octopuses' ink -- used to confuse predators -- does emerge from the opening that could be considered its anus. Perhaps another reason to try to avoid getting inked on by an octopus. (How do you do that? Don't startle them, scare them or make them mad.) But female octopuses also squirt the water they use to clean their eggs through this opening, so perhaps it's not all that bad.
And, according to Harmon Courage, Frank's video is right about one more octopus "fact": "Basically, everything they do is hardcore."