Ap Ezreal is one of my favorite roles in this game, Ezreal has a very powerful and malleable kit compared to that of other casters. Almost all of Ezreals abilities have a high scaling Ap ratio, the only that does not is Mystic Shot, having been originally designed as an ADC Ezreals Q has a low AP Scaling of 20% so its not as powerful (pre- Lich Bane) with Ap as his essence flux and Arcane Shift. When used with care Ap Ezreal can easily kite most champions in the league and burst them down with in a matter of moments. His Ult having an absolutely amazing Ap ratio of 90% can be used to initiate a team fight and bring almost the entire team low, or it can be used to snipe out that one unlucky ADC peacefully farming the bot lane. His Essence Flux has a large early game damage even with little Ap, and when maxed first can really chunk down an enemy laner. Essence flux can also help to either hit multiple enemies at once or assist in the siegeof an enemy tower with the attack speed buff it gives any allies it passes through. His E (Arcane Shift) Has a decent scaling and ratio of 70% Ap and can be used to initiate burst or to kite around the enemy since it is actually a longer range flash on a 11 second cooldown (in the late game). You honestly don't need to build any cooldown reduction on Ezreal since every Mystic shot that hits an enemy will reduce the cooldown of all of his abilities by 1 second. My one suggestion in playing Ap Ezreal, don't underestimate your damage output, But still play cautious, you can hit them whenever you'd like, but if you step out at the wrong time, or leap in. you're not going to last very long

As with most Ap based characters, last hitting is slightly more difficult when playing Ap Ezreal, Once you have Mystic Shot unlocked and ready to use in lane you can make use of it to last hit minions thus reducing the Cooldown of your other abilities and opening the way for more spamming of your basic abilities, but too much spamming can result in low mana at key points, so make sure to not overuse your Q and keep an eye on the amount of mana you have.

Mystic Shot with Lich Bane becomes a very powerful poking tool with a decent amount of ap, you can use that too poke an enemy down to low health around the minions since it has a longer reach than most other cast-able abilities

Essence Flux is good to use in the early game because you can fire it throw minions unlike most other skill shots, With the higher AP ratio it is the spear head of most of your damage, especially against multiple champions.

Arcane Shift is a great execution at the end of a fight, after jumping it will seek to the nearest possible enemy and fire a small bolt of light that will do 75/125/175/225/275 + 75% of your ap as damage as soon as the small bolt connects, so if you have a lower health jungler coming in too gank you, it can actually be productive in some cases to leap towards him and burst him before heading back to tower too b

TrueShot Barrage is Ezreals Ultimate Ability and playing him ap really makes Ultimate an understatement, It does 350/500/650 + 90% of your current ap as damage to the first target hit and 10% less to each enemy afterwards down to a -30% cap so if you hit the entire team with this ult, well, you do the math.

Notes-
- Spamming Mystic Shot is good to keep the cooldown reduction low
- Essence Flux can go through minions allowing you to poke enemies safely
- Arcane Shift can execute well, but should be used with caution
- TrueShot Barrage can deal a very significant amount of damage to an enemy
- TrueShot Barrage can clear waves with ease at higher levels and can be used to take buffs from a distance since it damages minions and reveals.