People have the wrong idea about Shadow Assassin Kayn.
Kayn is not like other assassins, his goal is not to kill one person and get out. Rather, you should be trying to kill 2 before dying. Now, let me explain. A Kayn jungle with Warrior enchant and Duskblade should be able to kill his first target without ulting. So, the optimal way to play Kayn in a fight would be to burst out the first squishy with Q+W+AA, then try to damage someone to ult on them (or ult on them straight away if you already damaged them). Then, you proceed to kill them if they are squishy, or kill a squishy close to them. If you successfully do so, it's basically a won fight, because even if you die, going 2 for 1 is almost never a bad thing.