Play Video
Please note this is a guide for those wishing to try off meta builds. I do not advise playing this in ranked. These builds have been tried and tested by myself and/or my group (NOOBN).

AP Jinx is a perfectly viable option fore other APC bot or Support. If you are going APC I like to play with an AD support like Jax or Jarvan just to buff her damage that tiny bit late game.

Her early to mid game is where she is strongest. Many people do not expect the 600+ damage from a Jinx E and will often kill themselves because of this.

In team fights when your cool down is low enough you can be placing up to 5 choppers per fight. With the AOE damage plus the CC it is a deadly combination when placed in the middle of the enemy team.

You can also surprise the jungler or mid lane when they go in for a cheeky dive under turret ;) You can get a lot of free kills that way.

Pros:

A lot of damage from E
No one Expect the damage so they often don't flash or dodge it
You can trap them in minion wave
Early game cheese
A lot of free kills
Amazing AOE damage and CC in team fights
Assassinate low hp targets

Cons:

Late game the damage falls off a bit
A little bit squishy
Heavily skill shot dependent
People can dodge
E is blocked by Yasuo windwall or Braum shield
High mobility targets can be difficult to hit

Early game all you have to do is farm. If the enemy ADC/Jungler/Support walks into your minion wave to fight E them and trap them there while you and your later attack them.

The best supports to play with AP Jinx are AD supports like Jax or Jarvan or supports with hard CC like Blitz or Thresh. This way you can place your choppers after the enemy has been stunned/knocked up/flayed and they have to either flash or give up first blood 99% of the time. If they flash do the same thing next time they go in for CS ;)

Mid game you want to try to get the bot lane turret however if your team is failing hard you can attempt to rotate to another lane and catch them by surprise with a well placed E while your team collapses.

Late game and in team fights you will want to fight either in the jungle or at locations with good choke points so that your E is more likely to hit. This is you main source of damage late game so it is important you hit these. The 600+ damage per E hit is extremely powerful and it is AOE.

AP Jinx is very team dependent.

When playing her you will need to stay alive for long enough in team fights to destroy the enemy team. Those well placed Es will do a lot of AOE damage to grouped up champions, but they will generally focus you so stay in position.

Early game you will need a champion with CC and late game you will need to be in position at all times.