Help our BrM monk!

[Rockets]

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.

[kaiadam]

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).