Hi this is h0tf0rteacher. In this guide I am going to give you some basics about middle lane Kayle.

[*] Push your lane early without losing cs if the enemy jungler has passive early game. Your opponent may lose some cs.
[*] Mid game clear the wave and get wolves, get back in lane clear the wave and get wraiths. Do this couple of times and you have a huge advantage.
[*] If you menage a good fight and kill your middle lane opponent having health and mana go gank bottom or bot. Remember if you get 1-2 kills you will became unstoppable. I remember myself wandering around the map having 5k golds.
[*] Don't afraid to use your ultimate on your team's tank or support in favourable situations.
[*] Always get second blue buff. If nobody really needs it keep getting blue buff.
[*] If you have a little money after your purchase and your blue buff soon expires buy Elixir of Fortitude. It grands you %10 CDR, with masteries and %20 from nashor's tooth your E will always be active.

Health 2230
Mana 1225
Armor 142.69
Magic Resist 35
Movement Speed 399
Attack Damage 103.7
Attack Speed 1,36
Ability Power 696
Magic Penetration 15
Cooldown Reduction 24%

Scaling Armor or Armor Seals,
Attack Speed or Magic Penetration Marks,
Scaling Ability Power or Magic Resist Glyphs,
Ability Power Quints.

Intervention> Righteous Fury> Reckoning> Divine Blessing

Flash and Ignite. I really can't see any other options.

Nashor's Tooth
Core item for Kayle with Spellsword and Righteous Fury at max you will give magic damage to enemies equal to 60+%60 of your ability power. It is like having a build in Lich Bane :)
So it is really worth buying it.

Rabadon's Deathcap
Best ability power item hands down.

Sorcerer's Shoes
Great for ability power champions. Berserker's Greaves
It is good cheap and great for kayle. Take it if you have penetration runes.

Lich Bane
Very good item on Kayle. Melts enemies in seconds.

Zhonya's Hourglass
It is pretty simple. Give you ultimate to your teammate when they need it. Use your Zhonya's Hourglass when you need it :)

Void Staff
Late game you will need magic penetration. You will eventually get this.