Pathing

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So Kayn has a pretty good clear speed and a healthy one so you shoud always start
Hunters talisman for the magic damage it does when you attack a camp with your abilities.
You have a few ways you can do your pathing with him you can do:
Raptors>Red>Scuttle>Wolfs>Blue>Gromp and then u should be able to pull of any gank with a good amount of heath but by the time you finish bot lane will be lvl 3 and you will be lvl 4 so you should look for a gank there

Alternative Path

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Now this path isn't as healthy as the first one was but i'll still leave it but it's more efficient and more faster way for u to get lvl 6 in some scenarios even before top laner you get aa couple of kills early
Patch:Red>Golems>Scuttle>Raptors>Wolfs>Blue>2ndScuttle(if your lucky enough to get it)>Gromp and by that time your golems are up you go an get them you get lvl 5 from them the Raptors are up and so are your wolfs and they will be able to give you
lvl 6

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Counter Jungling

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There is a few ways you could coutner jungle an enemy jungler the most effective way being the way of counting the cs and if u know that a specific jungler can't do let's say for an example raptors like:kha'zix,rengar,jarvan,etc...
those camps are yours to take everytime they spawn

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Ganking

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Kayn has one of the best gank patterns if not the best because of his E(Shadow step)
His insanely clear speed enables him to be dominant in the early game.However Kayn is not the best 1v1 fighter early on but he one of the most champ that are able to get out of sticky situations with his insane mobility.But once you get some item like:Warrior Duskblade(example for shadow kayn)and:Black Cleaver Spirit(example for red kayn)you will be the most terrifying jungler to ever fight.