When it comes to laning with kayn on top lane, for me I use blades reach to poke from a distance. This tactic is to try to keep the enemy champion at bay until you get reaping slash. This is because you dont want to over reach and get caught too far for you to peal from a early poke. After you hit level 3 and get shadow step this allows you to jump into walls for small heals if needed or to escape a 2 v 1. Upon hitting level 6 and acquiring umbral trespass, this is when kayn starts to become lethal. By the time the first tower falls, you should be almost done with ravenous hydra. This helps with sustainability and it give you an aoe basic attack.

Once you have ravenous hydra and ninja tabi you can leave lane or stay and farm minions. This is kind of risky which can lead to you being ganked by over extending into the lane. I usually leave lane once I have darkin form and 1st top tower goes down. I support other lanes to help them push as long as top doesn't get pushed back. By supporting other lanes this should boost you gold income and make bloodthirster fairly easy to obtain. After getting your bloodthirster buy black cleaver to allow for armor reduction of enemy champions making it easier for you or your team to finish them off.

by this time most towers have fallen except base defenses. This is when I pick up phantom dancer for the ability to move thru units. So that I dont have pathing issues plus basic attacks on enemy champions reduce their damage by 12% to me. I also pick up Guardian Angel for those big team fights, when I take lethal damage it heals me for 50% of my base health and 30% of my mana.

The main reason for top laning for me is the fact you normally face melee champions. I usually have my darkin form by level 6-8 depending on lane pressure. Once I have darkin form I am able to sway lane pressure due to the knock up of blades reach. A good kayn player can easily 1 v 2 same level enemy champions with this build. Also be able to turret dive without much concern in mid - late game. This whole build is based on life steal so taking a shot is not a big deal as long as you have something to beat on to get health back. The ravenous hydra also assists from taking a shot with its built in 100% base health regen. In big team fights umbral trespass can be a life saver with the life steal from gear and health restoration from the ability. A lot of the time I don't use umbral trespass as a finisher but more as a fight extender.