Kha'Zix Jungle Route

Honestly, with how nerfed he's been lately he really doesn't have any truly solid jungle route. The meager healing on his W isn't enough to keep you healthy, and he has to rely more on ganks than anything else. Until you get a Tiamat/Hydra your clear times will be abysmal.

That being said, starting with a leash on Blue might be the best option. He doesn't really need the Gromp buff since ideally you want to take as little damage as possible during your clear. Grab Blue for the mana regen and CDR so you can get in more Qs and more Ws. I played a match with him yesterday, didn't do too well because he's basically useless if he can't get in good ganks and I just plain couldn't, and was able to Blue > Wolves > Raptors > Red before having to go back to base.

My question to you is how you're ordering killing the minions in the camps themselves. Remember that his isolation bonus works on the large monsters in a camp, so killing off the little guys first will actually help you take down the big ones much faster and you'll take less damage in a slightly longer fight against the big guy than you would dealing a comparitively reduced amount to the big one and then picking off the little ones afterwards when they've all been attacking you. And try to make sure that when you use your W, you're well within range of getting healed by it. The heal isn't a whole lot, but not having it will still suck.

But like I said before, he isn't really in the best place right now. Because of how overwhelming he was a ways back, even though I never personally found him to be that big of an issue (honestly his power curve seemed pretty fair to me), he got nerfed hard, and they altered the way his Q evolved and his Isolation mechanic functioned, essentially gutting the majority of his power. Taking the damage reduction off of his ult, and lengthening the time between being able to use the individual stealths, made him completely and utterly useless in a teamfight unless the enemies were so low he could just hop kill reset around the fight to mop them up.

I've always loved the bug, but he just isn't very strong right now. The only times a Kha'Zix gets ahead is when his laners have enough CC to make sure people can't get away from him when he ganks, and if he gets lucky and snags a few early kills that he can use to stay JUUUUUST far enough ahead of the enemy players to beat them in fights. With the right teamcomp, sure he can be incredibly effective. But as it is he's more incredibly hit and miss than anything else.