If you want to play the Black side of the King's Indian then you want to be familiar with the tactical themes illustrated in the King Hunt from So-Nakamura Sinquefield Cup, Saint Louis 2015.
I discovered this game after taking advantage of the Chessbase 25% sale on the 29th Sept 2015. I took up a subscription to Chessbase Magazine for a year, and they gave a €40 voucher which I used to pick up the Bobby Fischer Master Class and Mikhail Tal Master Class Fritz Trainer DVD.
Danny King covered this game in the Chessbase video, and Nakamura's tactical finish provides great training material.
Training Position 1: Black to Play
Attraction plus King involvement in the mating net.
Make note of the swarm of Black pieces surrounding the White King, whilst White's pieces are on the Queenside.
Training Position 2: Black to Play
Taken from a hypothetical variation if Black had played 29. ... h3+!
Impressive is the tactical idea to attract White pieces to f4 and only then (with tempo), deliver checks with the Queen at f4 if needed.
The tactical power of two Knights hunting a King.
Training Position 3: Black to Play
This has to be intuitive if one wants to play the Black side of the King's Indian.
Illustrative of how Black's heavy pieces crash into the White Kingside.
Training Position 4: Black to Play
Hypothetical position after 27. Rxd7 Rxf3! 28. Bxf3 Qxf3 29. Qg2 Qxd3 30. Rd1
Outstanding example of interference.
Once Black finds his key idea is to try to play Nf4 (which takes the White Queen away from light squares g2 and f3) then this move flows.
Training Position 5: Black to Play
Hypothetical position after 27. exf4
The h4 pawn is an attacking piece for Black, participating in the deflection.