Example: a BrM with 50k AP before vengeance, using the normal-mode Immerseus staff upgraded to 2/2 for 8187.5 wdps. Let's also assume that you have enough chi/shuffle banked so that shuffle won't drop and you won't die because you failed to Guard something important -- ie. not what the OP's BrM is doing.
Blackout Kick does 7.12 * (adjusted weapon DPS + AP/14) damage on a single target. For a 2h this is just 7.12*wdps + 50.9% AP. In this example, that's 58295 + 50.9% AP.
Breath of Fire isn't a strike, so it ignores weapon DPS. It's just 1593 + 36.36% AP damage per target hit, or total 3645 + 101.4% AP if the dot can be applied.
1 target, no dot: BoK is unambiguously better. It has better AP scaling and also includes your weapon dps, so there's no question about it.
2 targets, no dot (eg. Dark Shaman): BoF does more damage if you're over 252k AP -- basically 200k vengeance. Might happen sometimes.
3 targets, no dot: (eg. council fights): BoF is better at 92k AP, so it's basically always worthwhile as long as one of the bosses is hitting you.
Including the dot improves BoF's AP scaling by a lot though, so what happens if you can hit adds with it?
1 target, 1 dot: BoF is better above 108k AP. This is trivial if a boss has hit you recently, and unlikely otherwise.
2 targets, 2 dots: BoF is better at 33.5k. This is now worthwhile even if you don't have any vengeance.
So I'd suggest as a rule of thumb: if you have boss-quality vengeance, use it if there are 3+ undottable targets, or 1+ dottable. Otherwise, only use it if you can get at least 2 targets with the dot. And of course the usual rules about not killing yourself by letting shuffle drop etc. still apply.
Breath of fire also runs off of spellcrit whereas bok runs off of melee crit: Over the course of a night of Garrosh attempts, I had 24.9% BoF crit (881 crit, 2648 noncrit) and 27.0% BoF tick crit (1250 crit, 3392 noncrit) vs 57.6% BoK crit (928 noncrit, 1261 crit).