The turbo I rebuilt was a Garrett t3, not that different... I'm not sure exactly how the KKK goes together, but that looks like it will work!
The things that I had a problem with in the T3 was that there were different ways to retain the thrust bearing, and thus slightly different thrust bearings. The first kit i bought was titled "300d turbo rebuild kit" that was a bumber when the parts were wrong
The compressor o-ring, or gasket, was way to large in the kit I got. I took calipers and measured the gasket surface and then ordered the seal through McMaster-Carr, the problem with that was I had to order it in a set of 25. so now I have 24 left over

I'm not sure if its the same dimension on the KKK, (they look to be similar size... just looking that them) if so, I'll send you one of my extras
once you take it apart you'll see its not that complicated and you'll see what parts to need for sure.