for those with success on kai'sa lets join together and post our beliefs in the thread.
Before i continue with this thread my number one belief is, stop picking kai'sa as a jungler. stop picking her in the jungle role. she takes up a team slot that could have a tank or an actual ap champion if the team is trying to go AP heavy. _Jungle kai sa is USELESS, STOP. YOU'RE NOTHING MORE THAN AN ANNOYING FLEA WITH SMITE STOP. Don't even bother continuing with this thread if you are going to keep picking her as a jungler. _
> i know the above statement is contradictory to the title of the thread but seriously kai'sa jungle is a waste of time. if you wan't to play an ADC jungler just pick kindred. You're way more beneficial.
first thing we have to understand she is most definitely a hybrid champ, capable of using both AP and AD items to mix up her damage as shown in her kit. Her W evolves, and even her auto attacks gain AP damage when ap is built. However the problem with building hybrid or even flat out AP is, her damage takes too long to ramp up if she goes hybrid or AP and her main source of ap damage (her W) is very easily avoided.
in this video its clearly a better option to go with the AP build but it costs WAY too much to go with the AP build. AD items are simply just cheaper and more convenient to build instead of going with the way more expensive build. Which is why you should just stick to building AD.
"BUT OTHER CHARACTERS LIKE 
CAN BUILD EITHER 
OR 
AND IT WORKS. THEREFORE KAI'SA IS TRASH AND NEEDS BUFFS!!!!!!"
ok calm down, what you need to realize is these characters are a lot more straightforward build wise when it comes to going hybrid.
-Jax gets hybrid his w passive and ult are buffed. All simple abilities that don't take long or much effort to proc. -Kogmaw mostly just auto attacks so his W which helps him auto attack more is buffed along with his ult, but his ult is not important. -varus... tbh i have no idea how this character works i hate him nor do i care to learn about him but as far as i can see his passive which gives attack speed on top of ap rage blade having both AD and AP means its pretty easy for him to utilize that partial bit of AP he has -Katarina, all of her abilities except her Q is AOE and also don't take long to proc.
So what about kai'sa? well not only does she require 100AP to benefit heavily, she has to get enough AD to benefit form her Q and enough Attack speed to benefit from her E. She has way too many options with way too many requirements to be made. Her W is blocked by minions and isn't small enough nor is it fast enough to be angled in such a way she can hit someone who is wide open. Anyone with decent reaction time can see her W and avoid it with ease which makes all that AP you spent stacking pointless.
As for kai'sa herself shes a purely reaction based character. You have to wait for your moment, you can't just go in guns blazing against everyone. Your damage mostly comes from procing your passive and that isn't something you just do on the fly especially considering your E has a delay which gives you a majority of the attack speed you need to start and proc your passive.
When farming minions in whatever lane you are playing, focus only on farming. you want to get as many minions to around just below half their health as possible and then use your Q then auto attack any minions that managed to survive. You WILL out scale and possibly DO more damage if you farm well and don't feed. If you absolutely want to fight you have to take note of some things.
Solo laning as kai'sa: make sure your opponent has used all of their cc abilities after they try to attack you or they miss their main source of damage. Once that is taken care of make sure you know where all of their allies are. if the opponent is alone go in but do NOT use your Q around any minions if you do, that is a good chunk of your damage gone. You also want to save the passive proc during or after you finish using Q. if you do too much damage right away people will realize they are in danger of dying and run away.
Bot laning as kai'sa: don't even bother fighting just farm, you're support most likely has no idea what kai'sa can do and will most likely use you as the scapegoat of the match once the enemy bot lane gets fed.
or 
should be your first items at least from my perspective
"BUT I NEED ATTACK SPEED TO"
calm down, you're first priority is farming. fighting is a secondary priority and if you don't farm well nor have the damage for your Q then you will just die and end up behind (you do not want to end up behind.)
if you absolutely want attack speed then go attack speed but farming is going to be way more harder and you won't do any upfront damage before your passive procs.
mid to late game you want to do your best to separate the enemy team as much as possible. Get as much vision as possible and bait out a split push, once people come running return to your team and see if you can pick anyone off before their allies can help. IF you can do that then you are all set.
that is as much info as i have right now feel free to share your own.
