@Gankyspanky
To start with, your cloak can be enchanted with multistrike.
Looking at logs you don't seem to be using plague leech at all? Pretty big dps gain getting 2 runes back every 25 seconds. You also didn't pre-pot, I know its only LFR but you used a potion during the fight so I'm just making sure you're aware.
Other than that I don't see any major issues with your dps, looking at statistics on warcraftlogs the average dps for LFR Butcher by DKs with ilvl 648-662 ilvl is 20k so you seem to be about where you should be. (Here's the link if you want to check it out)
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@Faylo
Looking at the butcher, his Soul Reaper uptime could probably be a bit higher but you guys have a pretty quick kill and it depends how long the butcher takes to go from 45-0%. If done perfectly he should get 1 SR per 6 seconds, however thats not always possible so you have to leave some room for error.
It also looks like he didn't pre-pot or re-pot during the fight, that makes a significant difference. He also only got 1 gargoyle cast off when he could have got a 2nd one off although it would have only been an extra 14seconds uptime. His dark transformation uptime seems fine.
I think his gear will be one of the main causes for low dps. Neither of his trinkets are that great but then again none of the Highmaul trinkets are amazing but when you compare the Grandiose Carnage trinket he has to something like Scabbard of Kyanos, its a MASSIVE difference. Having a 2200str on use that lines up with every gargoyle is very strong.
Weapons are the most important item for a DK, however the same can be said for pretty much every melee class. I dont know whether warriors or DKs scale better with weapons, I'd probably give it to whoever has the worst weapon.
As for twins yes he should be converting frost runes, if he opens with Outbreak > FS > BB > SS > Defile > Plague Leach > BB to victory he should be set for the fight, if the frost runes become unsynced then use icy touch to turn them back into death runes. (In the logs he did use chains of ice once, maybe he was trying to put frost runes on CD?)
He could probably get 2-3 more soul reapers in fairly easily on Twins and again he didnt pot at all before or during the fight.
To be honest he seems to be doing alright, just needs to pot, try get a few more Soul Reapers off if possible and learn how to manage runes for sustained aoe. And most of his gear is quite poorly itemized but it doesn't get much better until BRF for us DKs.
If you have any more questions feel free to reply or PM