We're going to maximize your damage with the Shadow Assassin form.
THE DARKIN SCYTHE(General Passive): Each instance of damage against champions causes them to drop an orb that are automatically collected upon leaving combat (including after Kayn's own death), filling a bar above Kayn's portrait.
Here's where things get interesting with Kayn, this passive also has two separate passives, two transformations if you will, that both do things differently.
The first transformation you will get usually will be the Darkin, Rhaast one which we avoid using since we cannot revert back to our original form and choose again, this one requires you to hit more melee champions than ranged hence it being easier to achieve.
The second transformation being the Shadow Assassin form which is the one we're aiming for and we'll be achieving this by hunting RANGED champions.
The second you receive the choice to activate your transformation, you will have a 4 minute cooldown for the other one, this means you cannot transform into the other unless you wait for the full duration of said 4 minutes, but on the bright side this waiting part is the key for us to achieve our Shadow Assassin form if we cannot get to any ranged champions during our ganks and fill our "Passive Bar" faster for this transformation form.
Rhaast the Darkin(Passive Transformation 1)
Kayn heals for 34.5% - 43% (based on level) of the post-mitigation damage that he deals with spells against enemy champions.
Shadow Assassin(Passive Transformation 2)
Kayn deals 12% - 44% (based on level) of post-mitigation damage dealt against enemy champions as bonus magic damage, lasting for 3 seconds upon entering in combat with an enemy champion, refreshing after 8 seconds out of combat with them or by using the Umbral Trespass(R) ultimate ability.
These transformations also change how Kayn does damage with his abilities.
This is the transformation we want to get with this build and guide.
REAPING SLASH(Q): dashes forward, dealing physical damage to all enemies he passes through before flourishing his scythe, dealing the same damage again to surrounding enemies.
RHAAST transformation: Both instances of Reaping Slash's damage are modified to 50% AD (+ 5% (+ 4% per 100 bonus AD) of target's maximum health) physical damage, capped against monsters.

BLADE'S REACH(W):After a short delay in which he can't perform any other actions, Kayn performs an upwards sweep with his scythe, dealing physical damage to all enemies in a line and Slow icon slowing them by 60%, decaying over 1.5 seconds.
SHADOW ASSASSIN Transformation: Blade's Reach's range is increased by 200. Additionally, Kayn conjures a living shadow at the casting position to perform Blade's Reach in his stead, allowing Kayn to perform other actions. (Basically this allows you to move while casting Blade's Reach)
RHAAST Transformation: Blade's Reach knocks champions into the air for 1 second when it hits.(You will still be unable to move in this form while you cast this ability)
SHADOW STEP(E):Kayn gains 40% bonus movement speed, is Ghost ghosted and can ignore terrain collision for 1.5 seconds. Immobilizing effects will interrupt Shadow Step.
Kayn heals himself upon moving through terrain for the first time and, if he's not in combat with enemy champions, Shadow Step's duration is increased. While inside terrain, Kayn's vision pierces all obstructions although cannot see into brush.
Entering combat with a champion after the effect is enhanced reduces the remaining duration to 1.5 seconds. The effect also cannot remain active out of terrain for longer than 1.5 seconds.(You will have to pay attention to a certain animation showing you where exactly you will be teleported back to if you get hit while inside terrain, meaning you might get teleported back where you first entered if you're still inside a certain long piece of terrain)
SHADOW ASSASSIN Transformation: Casting Shadow Step removes Slow icon slows and makes Kayn immune to them for the duration. Additionally, entering terrain will increase the bonus movement speed to 70% for the remaining duration. (The same effect where you get teleported to a certain point if you get hit while inside the terrain still applies to this form)
UMBRAL TRESPASS(R):PASSIVE: Whenever Kayn damages an enemy champion, he applies Umbral Trespass for 3.5 seconds.

ACTIVE: Kayn infests a marked enemy champion for up to 2.5 seconds, True Sight icon revealing them and becoming untargetable for the duration. Reactivating Umbral Trespass ends it earlier.
Upon reactivation or at the end of the duration, Kayn wrenches himself free from their body in the cursor's direction, dealing physical damage to the target.
SHADOW ASSASSIN Transformation: Umbral Trespass gains 200 bonus range and emerging from the target resets The Darkin Scythe's(Shadow Assassin's Transformed Passive) cooldown.
RHAAST Transformation: Umbral Trespass is modified to deal 10% (+ 13% per 100 bonus AD) of target's maximum health physical damage, and heals him for「 7% (+ 9.1% per 100 bonus AD) of target's maximum health 」

We're going to be maxing Q as our first ability by level 9. Grab points in W at level 2 and E at level 3. We're going to be getting our first point into W at level 8 due to the increased base damage it gives over the movement speed from E.

I've been playing Kayn since his release , he's one of the best junglers in the current meta that's not a tank. Yes that's right , we're going to expel Rhaast and make master Zed proud. This guide is not recommended if you have yet to master this champion in the art of dodging skills and making oneshot plays.
You're going to be the one to take your team into the mid-lategame,otherwise what's the point of killing everyone yourself am I right?

This is a build in which we go for mobility and damage over defensive items so we're going to be taking the Shadow Assassin form over the Darkin one.

You should almost always start with your Blue Buff since Kayn is cooldown dependent at the start of a game. You Could also start with the Wolves camp but I recommend to start with the Blue Buff so you can: A. either rush the enemy Red buff and smite-steal it and/or kill the enemy jungler at the same time or B. clear your jungle then look for a gank or recall for items.
You might not get the Shadow Assassin transformation before the 20minute mark since it requires you hitting ranged champions, but as soon as you do, this opens up a lot of new possibilities like for example using Blade's Reach(W) from inside the wall while still running at your target and finishing it off with combo of W+Q+AA(auto attack) with a Trinity Force proc.()

Pros
- Hard to catch due to low cooldowns and high movement speed
- High poke damage with W
- High burst damage due to being into assassin form
- Can position and reposition during a teamfight as needed
- Can easily hit the back line of the enemy team and completely destroy it and get out
- Smite can help us activate our (R) UMBRAL TRESPASS which makes escaping or assassinating easier

Cons
- Durability is a bit on the low side
- Trinity force , lethality items and Death's Dance are a must for this to succeed (I view this as a con since we're forced into a build we can't really afford to change)

(The reason i decided to go for the color BLUE for Pros is because of how extremely good this build is for what it's meant to do)