Ahoi my mates! This is my first guide so it might not end up as I want it, either way... I hope I make my point and this will help you.
This build is kinda different than the other and its focused on making more of a support Kyle that will definitely boost your team with quite an impressive AP and some AD as well. Basically this is a hybrid build and I chose this because Kyle herself is kinda hybrid, being able to AD carry, AP carry and Support.
I will explain some variations as well so at the end you can chose what's best for your play stile.

Pros:

Great damage output;

Great support for team

Has a great speed with her buff

Very powerful in early-game

An impressive farmer

Good for a solo-lane

Cons:

Squishy

Gets difficult to play mid-late game (Mistakes will cost greatly you team)

*She has to much useless armor and her...

Magic Penetration Marks
A very important boost for the AP damage Kayle has. (Could be replaced with armor penetration marks)


Seal of Focus&Glyph of Focus & Quintessence of Focus are very important for my build. Cooldown reduction is the only boost you can get for your ultimate and its of great use for the rest of the abilities as well. (Could be replaced with armor seals/glyphs of shielding/quintessence of fortitude for a better resistance)

Most people will start with boots and potions their build, but that seems pointless since you have your W (heal and movement speed).
An optional but important notice is that if you are having a bad time in your lane in early game because your opponent is harassing you, get a second .
Why early ? This is your life, your soul, your survival! Spellvamp healing you constantly with your E active and a very good AP increase.
: As I said before, cooldown reduction is very important since its the only boost your R could get. As a substitute you can use berseker's greaves for greater damage output.
: This item is your mana pool, attack speeder, cooldown reductionist and your ability power booster. It heals you and kills them!
: The most loved item in this game. I don't know how to say it simpler, it gives you everything you need.
: This is core for every hybrid build. Keeps you alive and gives nightmares to your enemy. Thanks to its active ability you will have another skill similar with your Q.
: This item is very rare for a Kyle guide. But I don't understand why. It gives you a lot of AP that you can use with W as well. People tend to use AD instead of this, making their W of very little importance. Oh well...
: You need some survivability in late game, and this will give you that. You can change it with , but you will lose some damage output.

Every skill you have has its own role. Using them in the right way will get you to victory.
Your Q its for slowing and damaging enemy champs. Try not to use it at farming.
Your W is for healing and speed buff. Use it on yourself for lane sustain and on allied champs with more DPS in teamfights.
Your E is your main farming tool and damage output. With cooldown reduction you should be able to keep it permanently active in mid-late game.
Your R is quite interesting. It keeps you alive, lets you run, helps ally champs. With cooldown reduction you can make a lot of allied people invulnerable a lot of times.

Don't try to kill enemies yourself. If you have an ally with greater DPS than you, buff him to do it! Victory of the team is far more important. (For example if you team a , and you buff him with constant W and R you can face up to 4 enemies, otherwise you will be outnumbered)

its useful almost anytime. It helps you escape, kill, and support teamfights. Definitely Core for Kyle.
This might end up being your last resort for escaping enemy gangs.

Kayle is strong early-mid game, very good for fast games.
She is not for killing, but for support.
Farm! Farm! Farm! and get rich before your enemies.

I believe screenshots are useless... so I won't put one.