in dominion. I went bot with a kages lucky pick, health and mana pots and a good 13 armor from my runes.

Die to khazix after one combo. Revived bought chain armor, made no difference died to one combo again.

I honestly don't see how any champion can withstand khazix. Even in a team fight.

tldr
khazix = win

If you've got to fight him, fight him in your creeps, so he won't get isolated Q on you. Also, you have way superior poke, wear him down and stay back, and charm him when he goes in.

Also, don't start Kage's Lucky Pick. Horrible starting item. Start P. Ring or Haunting Guise components, that extra HP pays dividends.

Also, Kha'Zix is very strong, yes.
It's not just Dominion, people are using Kha in 2,000+ Elo on SR as a mid laner these days too, judging from all the streams.

One does not simply try to 1v1 a Khazix early game as a squishy caster. I'm guessing by the time you bought your chain vest you probably had already fed him. Ahri shouldn't really lose against Khazix any way, understand, if you play a caster or an ad carry you can't sit there getting hit in the face, you have to kite, abuse your charm and ranged poke against him, you should also be able to push just as well if not better than him.

Tip for bot lane, don't try and kill AD Casters like Talon/Pantheon/Khazix early game as they will kill you and then they snowball just farm safely and wear them down with poke. Also if you're going bot get a Ring for 200hp and MP5, rushing BFT is nice and that but lucky pick is not really going to help you anything early. I haven't played Ahri in a while but she should be mana hungry if you're spamming poke, which you should be doing against a melee champ. Tip for midgame: Get Rylais, when he jumps on you, charm him and just kite him. Don't know what else to say, it's a skill issue, Khazix doesn't really have any advantage over Ahri.

I stopped reading at lucky pick. Yes, Khazix is a nightmare, no you cant blame him for your stupid starting itemization.

Boots Ring Red Blue works on most people. If you're going bot lane with Ahri vs KZ you will have mana problems, especially as he can quite likely zone you from mid health relic, so the blue pot is nonoptional. You'll probably be picking up a couple more blue pots as you back, until you get a Codex or something.

Think of it like in SR, I haven't played it in a while but weren't 2 Doran Rings pretty much meta for most AP Carries ? Prospector ring is basically your 2 doran rings.

2 Doran's or Catalyst into RoA, which delays the DCap, but makes you tankier and solves more mana issues.

I wouldn't start catalyst on Ahri - you need to kite, Ring + blues/morellonomicon will solve your mana issues, RoA is time spent not getting Rylai's/Torch which are core items, and you don't really scale off base mana.

That's SR, Volandum.
I was answering that double Doran's or a catalyst rush used to be the most common AP Mid build for a while there.