Sand King: "The Epi-Blink Initiator"

Just go to the jungle and farm stacks with Sand Storm and go for Blink Dagger after Brown Boots.
You can have it around 7-9 minutes. Only go to a lane if they need help or want to go for a kill on the offlaner or midlaner.

My same core items

I also feel like the first part of your summary should be in the introduction.

The guide just needs a little more formatting. Also playing Sand King mid and getting Arcane Boots, Blink Dagger, Aghanim's Scepter, Veil of Discord and Refresher Orb is the best and that's simply how I play him. I max Burrowstrike, 1 level to Sand Storm and Caustic Finale.

I don't agree with getting Vanguard, a Pipe of Insight, Mekansm or a Drum of Endurance would be more worth it and can also help your team.

I personally don't like this build: Sand King is usually played as a semi-support, and as such he doesn't get much gold early on. Considering the average time for a pair of Arcane Boots is 10-15 minutes and the Urn takes at least 5 more minutes, you'll get a very late Blink Dagger. Also, since the 6.80 patch, the Sand Storm has a huge area of effect even at level 1 and 2, so you can use it to stack and farm jungle creeps instead of soaking up experience in the lane.

After that patch, the "best" build I tried is going Boots of Speed into Blink Dagger, buying a Magic Stick (or Magic Wand if needed) for burst mana: you can double or triple stack a camp and, as soon as you reach level 3, go with double points in Sand Storm and farm it for a good amount of gold; repeat it three or four times and you can easily have a 15 minute Blink Dagger. Consider doing this in a trilane or with a carry that doesn't need much support like Weaver or Slark.

Please, add some formatting to this guide.