Upon getting bored playing AD kog, I asked myself why people played AP kog. The answer is simple. Kicks ***. I was very surprised taking whats nearly always used as an AD/hybrid champ and using it as pure AP. If you haven't tried it, give it a shot. Also, take mid. Your Q and E serve as a great harass and minion killer.

Mana. Your early game mana is important, and the other guide that I saw just had flat AP and no mana. Q uses 60 (a decent chunk) and your E uses 80+ (essentially non-spammable). The early game Fiendish Codex gives you extra AP and decent mana, and can be upgraded to Morello's late game. Taking mana regen runes will also allow you to skip Clarity and take Teleport for map presence and Flash becuase kog can't escape ****.

Survivability. I included Rylais because not only will you get that health and AP boost, but your Q will let you slow them down first, letting you approach and continue the slow with E, and help you hit them easier with R. Most squishies can't sustain more than 2 or 3 Living Artillery with built AP.
This is a conservative build, and if you're bringing down the house you probably wont need Banshees and can go with Deathfire Grasp or some other heavy AP item. But in most lvl 30 matches you'll probably want some defense, especially if you're mid and they know your capabilities. If you find yourself in a well-matched competition, you should be dying less or not at all, and will be able to launch more Living Artillery before having to bail a team fight.

Also, I started with E because if you're laning you can use it to hit bushes, hit multiple targets AND slow them. Seems to work.

With AD it is. Not AP. Most people dont build Q with AD and don't know how well it scales with AP. Always lead with Q, so your successive E and Living Artillery do extra magic damage.

While W is the crux of the AD/Attack Speed kog build, it's much less effective since you attack much slower and can spam R to do far more damage. Blue buff helps with this.

If you can't hit a moving target with your R, this is a useless build. This seems basic to pro Kog players, but like all skill shots, anticipate where your enemy is moving. For harassing purposes, don't use it more than once every 6 seconds or your mana will drain. In team fights, it doesn't matter if you drain your mana since you'll be going B after team fights 90% of the time anyway. Launch that **** all over their faces as many times as possible, hitting as many people as possible, and remember to use your E as a tripwire to slow runners.