Ho there S0Stronk.
Kog is one of the champs I enjoy very much. For him, I calculated a built that best fits my style and I have a lot of fun with it:
Marks and Quintesseces (Atk Speed): +25.5% Atk Speed
Seals (Flat Armor): +13 Armor
Glyphs (MR/Lvl): +24 MR at lvl 18
Items (they are not in order):
1) Madred Bloodrazor (DPS and armor)
2) Malady (DPS and lower MR)
3) Abyssal Scepter (Resist and lower MR)
4) Berserker Boots (DPS and mobility) OR Phantom Dancer (lower mobility but higher DPS)
5) Frozen Mallet or Rilay (Surviability and slow to keep your foe more time inside range)
6) FREE (Nashor Tooth or Black Cleaver usually)
-Cleanse (to scape from CC)
-Ghost Walk (to run when not attacking)
The key point of this build is to use your Q along with Malady and Abyssal, to drop your foe MR by -69; Usually if your foe don't get MR items, you will set him into negative, and with your %HP damage will make it melt in few attacks.
I don't care much about mobility with items. The time you are attacking you can't run, so, I prefer to have my main speed boost via Ghost Walk and use items for damage and resistances. I often swap boots with PD. If you get PD as boots, you can even sacrifice Nashor from "Free" item and grab Trinity instead. Trinity can give some physical damage with the Sheen active and some more HP.
With this build you don't have the lifesteal sustain from the Physical DPS version, but you can kill even faster. The secret is good positioning. Of course, it works better with a competent team. Your lack of sustain could work well with a support and/or tanker protecting you.
If I remember right, when full built at lvl 18, I had arround:
110+ Armor AND MR
2.3~2.5 Atk Speed
That's how I like to play him. I am not saying it's the best way or better than the physical damage one. I just find this setup effective, fun and that it fits his design better.