I have been playing Kayle for a while now and after playing her with triforce+infinity edge, I created a new build, relying on the same item: Sheen.
You start with Saphire Crystal. When you have 820g you go back and buy sheen (play nice and safe, getting last hits and reckoning crazy champ)
Then, your game shall start. Use Sheen's proc as follow:
E->normal hit->Q->normal hit->W->normal hit->Q->normal hit etc...
If you managed it right you've just killed those 2 champs that stayed too much on the lane.
There is nothing stronger than a level 6 kayle with sheen (if the other champs are lvl 6~, that goes without saying)
Once you get that money, get Boots of Swiftness or Berseker. Let me stop a sec here: BoS are cool if you are confident and a bit skilled. Combine them with your ulti and you can get a kill that would have been suicidal to go for for any other champ and come back alive. Needless to say, you have to manage your tower-dives. The berserk boots on the other hands are useful, because kayle hits slowly without items. I just find that Movement Speed is a greater advantage on the enemy than a bit more attack speed, but that's a personal point of view.
At this point you have to make a choice: either you go for Trinity, either you go for pure AP destruction.
If you are confident and want to go for the Ultimate Angel of Fury do as follow: First buy a Mejai Soulstealer, you must fill it so go outside and kill! If you are not late, didn't feed and know your Kayle, Sheen+boots should be able to grant you a few kills between level 6 to 12.
Once you have Mejai, focus on building Lich's Bane.
Then it's your choice, depending on the way the game goes. If you get feeded and the game isnt that late you can go for a Rod of Ages.
If you're having trouble filling your Mejai, then aim for Zonhya's Ring.
If you're struggling then a
Nashor's Tooth is also an item you should consider buying at some point.
At the end you should have around 300 AP (or way more) and will do 600+ crits, Reckoning and Righteous Fury will be very, very deadly.
The worst thing that could happen is that you can't get that Mejai filled and can't gather all the money. Another sad thing, if you get a good start with this build, you'll probably won't see the end of it (/surrender).
I admit that it is a risky build but it is a very fun and surprising way to play Kayle. And compared to a DPS-oriented build has a similar outcome.
Here's my views on the matter, I'll be happy to read your comments now.
PS: Pardon my english, I'm french.