Rumble just takes finesse to beat. Most Rumble's will beat kha'zik if played right but it's all about being able to scare Rumble. MOST and i say most because some Rumbles aren't easily freaked. But if you engage on him early and keep it up without acting afraid of his Q. Aka, running away from his Q. Lots of Rumbles make the mistake of turning back as a counter measure thinking "oh he's gonna out dmg me".

Last rumble I played again I was teemo top and frankly Rumble should have flat destroyed me. But he tried to jump at me at lvl 3 and I just stood still AA him until he turned around and when he's running Rumble can't really do anything.

It's a good idea to stick near your minions because if his Q is his only damage output then it really affects his poke-run kit. Avoid the harpoons, sacrifice some health to take some Q damage and just return it back to his face twofold.

it's because fire is super effective against bug

Necro'ing this post to update.

Just played Kha'Zix vs. Rumble top and I have some insight. Establish lane dominance early at level 1. Zone the rumble like you have pressure on him, and most of the time he'll respect that and play passive, farming with his spears. Even if you clearly don't have any lane dominance, a good act will convince the rumble to let you farm a few levels where you can actually pose a threat.

I started 11 health pots + ward
First buyback was a Hexdrinker, more health pots and 2 wards.
Transitioned into an early Giant's Belt, and sat on that while I built damage next.

Good luck!

lol

Kaz actually destroys rumble - like has been stated - be aggressive and he will have to respect your zone. He can harras you with harpoons all day cause hell mostly miss and then you jump to him and win the trade everytime. Don't be afraid of his q. your AA and spell out dmg him early on.once hes 6 its a different story and youll have to back off a bit - but at this point you are better off ganking other lanes and he cant really hurt the tower quickly and when hes extended gank him with your jungle. KAZ is probably one of the stronger plays vs rumble because he cant just escape you with his w.

i beat rumble with teemo, so it cant be that hard