Hey, this is my Yolo-Yellow Ezreal build, I Start play him couple weeks ago and try to make an effizient build which is not mainstream. I try couple of things and find out that this combination works pretty good. You just need to get to your Statikk Shyv, with a normal support you should be able to outdmg the most of the adcs.

Here are some Bot-lane combs which can work pretty good:
-Ezreal + Nami: Works pretty well because you build late lifesteal and she can heal pretty well, also her dmg boost goes well with your Q
-Ezreal + Nunu: Its poke over poke over poke, and the attackspeed buff is pretty nice
-Ezreal + Nidalee: Heal (Attack speed) + Poke, nothing to say about
-Ezreal + Leona: Her passiv goes really well in the early and mid game, your Q will deal tons of dmg

All in all you can play Ez together with any Support, you just need to know where you have to possition yourselfand you need to know how much dmg you need to take down your enemy in the right moment.

Statikk Shyv: Normally I just build it on Ashe, but I figured out that it works on Ezreal pretty well. Your farming is easier and you can poke your enemy more and more. Also the Crit is really nice.

Trinity: Nothing to say about, its a must have.

Berserker Shoes: You could switch to shoes with MR or Amor if you want to (depends on enemy team comp).

Inf Edge: Crit Chance of Statikk and the extra dmg from the trinity, combined this with the Inf edge will deal tons of dmg.

BT: Thats something you need in every teamfight or to duel the enemy adc.

LW: Amor pen, nothing to say about.

Tristana: should be an easy matchup for you, Poke her or burst her with a full combination together with your support.

Vayne: Thats something I figured out in my last games, you can duel Vayne in the Late/End Game if you Position right and hit your abilities.

Ashe: more difficult cause most of them also build Statikk, she will poke back, be sure to hit your skillshots and dont waste your mana too much.

Caitlyn: Hard in the early, but you can take her in the mid/late game out.

Jinx: Difficult to get ahead in lane against her, but you will outscale her in the lategame.

Lucian: I Wouldnt pick Ez into a Lucian, because the build isnt really strong in the first couple of lvls and trades, Lucian will destroy you.

Draven: Much Dmg, much utility, its a Skill matchup.