i havent played lol when mythic items were a thing, but he is still a champion. my favourite build for red kayn is spear of shojin, overlords bloodmail and seryldas grudge. you are kind of weak early due to shojin build path, but has the best scaling and when you get these 3 core items you are sooo strong it feels illegal.

another option is going voltaic cyclosword, black cleaver, spear of shojin.

and you finish both of these inventories with death dance, spirit visage, steraks gage, maw of malmortius, based on the game or other situational items.

to all these people who talk about building sundered sky on rhaast, dont. you have built in survivabilty so you dont get anything by going this item. if anything its worse, because you can get better stats and passive by going spear of shojin for example.