Splitpush the entire game, or go mid if the tower is accessible.

Run it down for turrets. KDA does not matter, you will be loaded with gold. Sacrifice your life for turret damage, it will be worth it.

With this build I have not once failed to score within the top 0.1% of turret damage as Tahm Kench Top. And i'm terrible at this game.

Repeatedly R for any exposed inhibs. Make sure inhibs die as quickly as they respawn.

Back door as soon as the nexus turrests are accessible and there is no one defending. Otherwise, bring an ally in your R. The limit to a double push like this, if you have the right ally, is usually a sungle inhib, both nexus turrets, and then the nexus itself.

Passive:
Kench's passive makes his autos hit harder based on his max health, which directly benefits both his wave clear and his tower damage. Building health also benefits his demolish procs, meaning that kench is a rare case that can demolish turrets like a tank and melt waves and inhibs like a marksman with the same build, all the while remaining tanky enough to more than hold his own in duels.

W:
Kench's W allows kench to rapidly clear waves.

R:
The most relevant ability to this build. Kench basically has access to a second teleport, and this one does not require him to have a target to teleport to. The ultimate tool that allows kench to back door and pick off inhibitors in a way no other champion can manage

It doesn't matter, any matchup is fine. Even if you turbo int, you will still be able to hard split all game and win.

Even with this build, you can absolutely duel the **** out of most top laners from the start of the game until the start of the late game