On kayn when wishing to go either form i will almost always start red with a leash preferably then go to krugs over the wall then clear raptors into wolfs into blue then gromp into scuttle then gank/reset (depending if a gank is possible. But if going blue kayn and wishing to start a specific lane you can do a 4 camp clear wolfs raptors red and then krugs into a gank either bot or top getting level 3.

Depending on which form you decide to go on kayn his playstyle is very different on Rhaast you need to farm until an item lead and focus on frontlining in teamfights and protecting you carrys/peeling. But on Shadow Assasin (blue) your entire goal is to eliminate the enemy carrys (usually their adc or mid) by staying out of site until the fight begins and then flanking in to one shot and then backing out to wait for cooldowns.

Usually i decide to go shadow assassin if the enemy team has 3 or more squishy/ranged champions and go rhaast if they have 3 or more tank/melee champions but when deciding which form to go keep in mind that some lanes are easier to gank then others and some champs say they have a lissandra midlane as their second ranged and rest of team is squishy-ish but you would have to keep in mind the difficulty that comes with ganking a lissandra

There are some mechanics on kayn that are very helpful whether its in jg clearing or in a fight some of his clear mechanics ae him being able to q into a wall and not go over it to end his q animation quicker and get his double damage off faster also being able to solo both gromp and the blue sentinel at that same time. There is a useful bug on the odyssey kayn skin which makes blue kayns w appear invisble to the enemy when kayn is inside a wall when he uses it still afflicting the damage but not appearing visible to the enemy. Another good kayn mechanic that is extremely helpful and used every game is in a fight you can use blue smite to mark an enemy to ult them this is especially usefull on blue kayn as your ult range is larger.

Preferably start red and if your team gives u a leash good if they dont its fine just puts u behind in clear speed a bit but after finishing red level e second and e over the krugs wall and use q on both then focus big krug down then q all of the 3 medium krugs and kite to q all of the small ones again then walk/e to raptors autoing the front one then q to the back, focus large raptor and then q again to finish them off then level up q again as w is not needed unless fighting. Walk to wolves q all three of them auto the big wolf two times then e to blue buff and auto blue two times and q all of the wolves to finish them off again then auto blue again then walk to gromp and kite it to the middle of the blue and gromp spawns and then use q and smite to solo both at the same time without them resetting. If the enemy jungler ends up on the same scuttle as you dont contest as both of your smites aare gone instead go straight to the uncontested scuttle on the oter river. After this you can either go into a gank on any of the lanes, invade the jungler on a side they havent full cleared yet say you're vs a rek sai you know they wont have cleared their krugs on their first ful clear as she would usually do a 3 camp clear (red blue gromp. Using jg knowledge of other champs clears is crucial when invading as you know what level they'll be and what camps they have cleared adn what side of the map they will end up. Another thig to do after your full clear is if there are no available lanes to gank you can clear back into your redside jg and clear krugs then raptors and reset having enough gold for ironspike whip or serrated dirk depending on the form you wish to go.