since jinx's nerf, be careful of how much you use your abilities in lane, since you can miss out on a lot of kills if you don't have enough mana (last hitting with fishbones when they are under turret, zapping them, or ulting them)
jinx's e takes a second to activate so placing them on yourself or a little in front of the enemy champion is better than directly on them.
when you are ulting to snipe, try to do it out of sight so the enemy doesn't hear you / see the animation and get ready to dodge it
use your rockets to poke enemies when they are coming in to cs by attacking the minions and letting the splash from your q to do damage so that you don't get minion aggro
rockets are good for teamfights / champions that are out of range, minigun is amazing when someone is on you.
Buy BF sword into Hurricane into IE into RFC - even if you are behind, you will deal insane damage
If multiple people are on you (and they all have full health) use your minigun to kill one person (your hurricane should poke the others down a little) and use you passive / flash to re-position
you can switch guns faster while you w, but do this mostly while you are chasing (eg, rockets, w, switch to minigun while they are slowed and catch up to them in order to e and finish them off)
it takes a while to figure out your limits with jinx since she is squishy with no escapes; the best way to learn is playing her against every match up and knowing how to be aggressive / passive at the right time.
getting a kill is not worth dying unless it is a double or something. There are times I tower dive adc / supp after killing the other in order to get the double, but generally going 1 for 1 is not a good idea. Jinx is powerful whether she gets fed or not (and by late, even if you were 0/2 in lane, you eventually come back and get fed too) but if you feed the enemy team, they have a better chance of bursting you at the very start of teamfights.
Also for the masteries, I've tried Warlords against pokey lanes and they have helped me survive, but I prefer fervor.