This isn't a revolutionized Jinx (like lethality varus). It's an optimization where you try to use everything you can to your advantage.

Spells:
Flash+heal. Movespeed + heal for support (or other teammate) is just insanely helpful since you're very immobile. You'd also prefer if your support is running ignite (read Synergies).

Flash+exhaust. In case the enemy team is running Zed/LeBlanc mid and Akali top or something along those lines.
Also if the enemy ADC is Tristana.

Flash+barrier. Basically just if your support insists on going heal.. really not what you want

Items
You'll want to get early boot of speed to help with your immobility. An early BF is also great if you've got the money (always great on the first B). Then hurry and get berserkers greaves + inf (inf first if you got the money but you'd rather get Berserkers than cloak of agility).

Next up you get hurricane to finish your core build. Now you've got the core stuff. You'll want those 2 first, always. Only exception is against Soraka/Yuumi where you'll squeeze an executioners in somewhere.

Now get Bloodthirster. Most guides will recommend you get more crit (PD or RFC) but that is NOT the case with this build. The reason for this is your W. It scales great off AD (not crit) and I know some of you will be thinking "It scaled better on release". Which is true. But it is still very very viable if set up correctly.

Occasionally you might need GA early but generally just get the BT. Will also make it impossible for tanks to kill you unless very very fed. Then get 1 more crit item (either PD if you're scared of dying or RFC if.. you're not). Same thing for GA/Dominiks/Mortal reminder. Get the one you feel you need the most. In my experience it'll often be GA. You could also switch out PD/RFC for the dominiks/mortal reminder. Really just depends on the flow of the game.

Runes
Sometimes nimbus out for absolute focus since Bloodline and third item bloodthirster will keep you healthy but otherwise it's pretty standard. The key of this build isn't to revolutionize Jinx, but to optimize how you become JINX.

General
Jinx W has one of the higher base dmg + AD scaling of ADC's and you should exploit it with a CC support like the mentioned to snowball. As a hypercarry with Get Jinxed as a passive for immense team fight pressure and clean up you'll quickly become unstoppable if you can get just a little bit ahead. Maxing Q only offers you a slightly improved attack speed and +25 range per level. Each +25 range will do literally nothing as it helps you outrange no one. And by the time it does (lvl 7-9) the lane has already been decided. So you might as well take it second and go W for the burst damage + poke(if you learn all the small finesses, e.g. if they stand between the turret and the outer wall they can't dodge it and this happens even in diamond+ or just generally when they're up against a wall and you align yourself with them).

You can also snowball off a single cross map R on that lucky toplaner/midlaner. Who, as a bonus, will also be tilted. So keep your eye out for these guys and learn to read backs (often they'll recall about a rocket size behind the turret - this goes for all elos).

So get out there and start shooting!