AP Kennen obviously benefits from anything that gives AP or reduces cooldowns. He also needs to have a fair amount of survivability in order to effectively utilize his ultimate (Zhonya's Hourglass is popular for exactly that reason). Sheen is strong on him given how often he fires off his skills; following up with the auto-attack provides that extra layer of burst damage.
Zeal (the second part of Trinity Force), however, gives him nothing at all except some move speed... which he gets through Lightning Rush anyway.
Phage is nice-ish for its health, but the extra attack damage and the on-hit slow effect aren't very helpful. This item is surpassed on him entirely by Ryeli's Crystal Scepter.
Once you build your Trinity Force, the Sheen effect gets stronger, but you're spending a lot of money for that benefit. Lich Bane has the advantage here because, as AP Kennen, your AP will be much higher than your AD and you get the advantage of suddenly doing truckloads of AD from Lich Bane procs.
In short: Don't bother with Trinity Force. Lich Bane is a superior upgrade of Sheen, especially with other items you should seriously consider (Rylei's and Zhonya's).