Pros
Kill a lot more minions meaning more gold and experience
Your auto hits will deal more damage meaning you are more likely to get a killing blow of it plus when fighting champions you will take it down faster.
As this build is hybrid, your Arcane shift, Essence Flux and Arcane Barrage do more damage as well.
Cons
Your Arcane shift, Essence Flux and Arcane Barrage do less damage compared to a pure AP build.
Overall: i like this build because all 4 spells do a good amount of damage compared to an AD Build where mystic shot and auto hits does good damage or an Ap build where Arcane shift, Essence Flux and Arcane Barrage do good damage.

Ignite and Flash are the two spells i use when playing Ezreal. Ignite is always a useful option as it does reasonable damage and can also do that last little bit of damage needed to kill an enemy.
Then second spell i selected is Flash. although some people say that Flash is useless when playing Ezreal because of arcane shift, i think that it is a actually a great choice. This is because the Cool down on arcane shift is rather long, so when you get into a sticky situation flash can give you the little bit of distance you need to escape.

If you dont like Flash i would also consider using Teleport.

Tips.
Ezreal is a hard Champion to play, he is in dire need of a buff that he will most likely never happen. But that doesn't mean he cant rape :D.
there are a few small tips that i would recommend trying.
1. Mystic shot costs little mana, so try and use it whenever you think you might hit the enemy.
2. Arcane shift should be saved, dont use it at the very start of a fight, because if the tables turn, it might be your only way to escape.
3. Ezreal is a squishy champion, so make sure that you stick back, and whatever you do dont get blood thirst, because it will just end up causing your death.
4. If you want to steel a kill Arcane shift is a really efficient way of doing so, just dont use it in a team fight because of point 3.
5. Dont Jungle, it doesn't work.
6. Essence flux is a great harass spell, if you are going mid i would get it 2nd instead of Arcane shift.

This build is a really good all rounder, you will hit like a truck. you can solo great or share a lane just as good.

This is my first build, but i have been playing Ezreal for a long time, and this is just how i like to play him, so i would love some feed back :D thanks guys.