Sup peeps. This is a build I've worked and battle tested and it works great. I'm new to the site so if you have anything to help me improve this/future guide please post below. I think everyone for their patience and time reading this guide. Hope I'm not stealing someone elses build :D.

This is a dps Kayle build that's monsterous in late game. Early game you might have some problems due to being weak in early game. Patience plays this build.

Pros
Excellent late game
Decent farming
Still keeps part of her support, making her a great teammate through her healing and invulnerability spells
Cons
Sort of bad early game
Only decent farming
Very item costly

Greater Mark of Insight- Spell pen is great for this build since you're gonna be using the hextech gunblade for not only damage from AOE but also for vampirism. Anything to help you stay alive.
Great Seal of Replenishment- Kayle is a mana guzzler. You need these.
Greater Glyph of Potency- Extra ability power per level never hurts.
Great Quintessence of Vitality- This will help your late game by a lot by being able to live.

Reason why I chose these masteries is mainly for the mana regen. The mana you'll be using will not only make you cry at times but will also determine your ability to kill. Plus extra xp will help you get your skills and your runes up faster for added benefits. Cooldown reduction is a little important to along with the spell power. Using her invincibility shield a lot will help you stay alive in seemingly impossible fights.

Doran's Ring- Start with this. This will help your mana regen in early game, enabling you to use some of your more potent abilities such as Reckoning and Divine Blessing.
Health Potion- Why not?
Ionion Boots of Lucidity- Helps with your cooldown reduction by 15%. Great for constantly spamming abilities. This is why I take a lot of mana regen.
Guinsoo's Rageblade- This is your main item for kayle. It gives you both ability power and attack damage. This is great for Righteous Fury.
Nashor's Tooth- Added attack speed, mana regen, and even cooldown reduction. This is all the cooldown reduction you're gonna need. This helps a lot with harassing other players with Righteous Fury.
Hextech Gunblade- This item is awesome for kayle. Gives attack power, ability power, and spell vampirism. This helps Kayle out with all her abilities by a drastic amount.
Trinity Force- Buffs everything kayle will need. Also give her increased movement speed and slow, for catching enemies.
Lich Bane- More mana, ability power, increased speed, and extra damage all around. Just like Trinity force, this is everything Kayle will need to slaughter.

The sequence is kind of slow in the beginning but, will get better as the game goes on. Harass with Reckoning and farm/harass with Righteous Fury. This is very late game material.

Flash- Good for catching/evading enemies. Kayle will have a lot of mobility with this and her items.
Clarity- As stated above, she is a mana guzzler.

Other considerable spells
Ignite- Get some early game kills with this doodad.
Ghost- Some people find it better than flash in certain instances. But your Divine Blessing will increase your speed to.
Exhaust- Very good for pesky melee dps.

You can assume 2 rolls at the same times as this build. Extra ability power allows you to heal greatly, invulnerability spells also help for tower diving/ living through an unwanted battle. But you are a killer, you feast on the weak and destroy them with high amounts of dps through both ability power and attack speed/damage.

Kind of hard yet can be done moderately. Your farming isn't going to exist that much until you get your first 3 main items. Then you rack up gold fast than most characters i've ever seen.

This is a great build that can work as long as you play smart. If you have suggestion/comments about anything in this guide please share as long as they are actually beneficial.