Super Shredder Kayle: Attack Speed, Damage, Shred. This build is extremely fragile. The idea is to rely on invincibility to protect you while you strike them down, then you escape using Kayle's W.

Boots of Speed (level 3 movement)
Ionian Spark
Malady
Black Cleaver
Phantom Dancer
Infinity Edge

If you want a little more armor and resist I recommend relying on magic damage like so:

MagiKayle

Boots of speed
Ionian Spark (Attack speed, magic dmg)
Malady (Attack speed, magic shred)
Wit's End (resist, attack speed, magic dmg)
Void Staff (% magic pen)
Madred's Bloodrzrs (armor, %health magic dmg)

I haven't tried playing a tanky Kayle since she doesn't scale off of armor, resist, or health, but if you absolutely demand more defense I highly recommend building armor and resist (Thornmail, Force of Nature) insead of health-stacking items (Warmog's, Frozen mallet) because Kayle has a heal, so armor and resist will make her health more difficult to remove.