AKA, The "Twilight" Boss or the Cullen Brothers Boss.
You know, of course, that these are three haughty blood princes that we've seen before ("Naxxanar was merely a setback....."), that they share a health pool but that only one of them - the Empowered One - can be hit at any given time.
There's a lot going on, as each of them has their own abilities, but fortunately you can ignore most of it during the fight.
What do you need to pay attention to, and how do you best do your job as DPS DK on this fight?
Well, glad you asked!
Essentially this fight has only two requirements:
1) Don't die to the few actually dangerous things in the room, and
2) Do a modicum of dps to the appropriate boss (not even a dps race at all, really).
Pull/Phase One: Summon your Army pre-pull, but DON'T pop your garg/drw/ghoul on Valanar, unless your guild bloodlusts/heroisms on the first prince. Ours waits until Keleseth to heroism due to the Empowered Shock Vortex that disrupts dps on Taldaram, and the fact that due to Keleseth's constant casting, he's unable to dodge or parry any attacks.
Valanar: Speaking of the Empowered Shock Vortex: That's BAD THING #1 on this event. Just make sure all melee know which direction they're running consistently when it casts (we call out 'north,' 'south,' northeast,' etc in melee channel), because it's very easy to kill yourself or others. When the Shock Vortex isn't empowered, it's not very dangerous, but it is annoying if it's near the prince you're dpsing - stay away just to avoid the knockback. Don't worry much about his Kinetic Bombs since that's likely to be a hunter or caster's job, but if it's near the end and the bomb person goes down, putting your ghoul on a bomb, or tossing an Icy Touch at them can keep them off the ground for a while. Otherwise, just hit the effete fellow as much as you can in between Vortices.
Taldaram: Prince #2's main attack is the Ball of Flames, but it won't target you as long as you're in melee range, so get on him quickly once he's empowered. On 10-man, you may need to follow Balls for a bit to attract a few glittering sparks, but we don't bother - as long as the target kites the Ball, everyone should be fine. BAD THING #2 is actually Taldaram's frontal cone fire attack. You should know this by now, but NEVER dps Tald from the front, even if a shock vortex keeps you away from his behind.
Keleseth: Prince #3 casts Shadow Lance, but you can pretty much ignore him as the tank should be taking all the lances - and if the tank fails, you're likely doomed anyway. In dire circumstances, you can grab a couple Dark Nuclei and try to tank Keleseth briefly while awaiting a battle rez for the regular tank. But otherwise, like the others, just hit him when you can, and summon garg/drw/ghoul when heroismed. A personal pet peeve is when the Keleseth tank doesn't move the prince away from a shock vortex, so all my cds get wasted, but again, that's a communication and tank issue more than a DPS DK issue. BAD THING 3#? Honestly, I can't really think of such a thing for us DKs...
To sum up: doing your job to the best of your ability means dpsing the appropriate prince and switching crisply between them to the one with Invocation of Blood, and avoiding things that will kill you or others (although most of these are others' responsibility, or are fairly inconsequential). MOST IMPORTANTLY, run away from others during Empowered Shock Vortex. Sorry to be unable to offer many more 'tricks' to this fight - there just aren't many.
Even with running around so much, DKs should do well compared to other melee (ranged have several advantages). As with Putricide, just anticipate and switch quickly, and you'll do fine. This isn't a burn fight at all, so don't expect to do too much more than 7k dps. If you avoid careless or foolish mistakes, you'll be fine, and the Princes will bite the dust.