Your game plan early is to stay back and don't die. Try to farm everything you can and safely proc klepto with E. It is very important to get a feel for match ups and your damage early on to know what you can and can't do. You will find there are situations where your early game can poke well.

Once you start getting your first and almost second item you should still play somewhat safe depending on how far ahead you are. Around this time though, you are useful in team fights, which is what makes this build better than other attack speed or on hit builds. You can now kite fights hard and throw out q and e for burst and speed your allies up.

At this point your burst is strong and cool downs low. try to not get picked. Poke as best you can but make sure you can kite back to your team. In team fights, you should throw out q and e then back up and repeat. use ult when needed.

I am still actively working on this guide, but after play testing a lot of Kayle so far, this build seems the most optimal. It covers her bad early game a decent amount and gets her online much faster. With an attack speed / on hit build, the early game is weaker, it scales slower, and when you do scale you still just walk up and die. With the ap build you can kite harder because you don't stand in front of the enemy team constantly. You can get burst down and go in and out.