EDIT 9/5/12: After noticing the amount of crits this build gets, decided to change the 10 points in Inventions to 10 points in Explosives. More burning, longer burning.
EDIT 9/19/12: Updated build to follow along with the change to Juggernaut. Changed the Firearms grandmaster trait to Juggernaut because it's a must now. Changed Alchemy grandmaster trait to Backpack Regenerator, though you're free to change it to Cleaning Forumula 409 if you prefer.
Mobile fiery death! Let's go over this:
You ain't using this. Sorry. Save maybe for an emergency getaway with Net Shot, Overcharged Shot, or Jump Shot. Maybe.
Standard healing. Ballin.
Put a little pep in your step, and unleash the fucking inferno. Fury, Might, Retaliation, Swiftness.
Your choice what you want to put here. Elixir C has more applications for PVE, but if you're doing PVP I'd recomend S or Utility Goggles here. Basically, it's your "Not today!" slot. Elixir U has little use here. Again, with H.G.H., more Might. Also, if you have a lot of conditions and you pop a C to turn them into a lot of boons, that's all the more damage you'll be doing due to Energy Conversion Matrix.
Forget everything I said about Elixir U. It's so much fun and racks up burning and vulnerability like no one's business.
Your bread and butter, with salt and garlic, even. Never unequip this. Learn it, live it, love it. Some pro-tips:
1.) The first thing you should do when you equip your Flamethrower is immediately Ctrl + Right-click on Flame Jet; this should always be auto-attacking.
2.) Napalm behind an enemy or cluster of enemies, and then push them through with your Air Blast. They'll end up going through the wall of fire twice as they try to get back to you.
3.) Flame Blast will not explode if you use it up close to your target. I don't know if it's intended or not, but the gob of fire seems just fall to the ground and go away once it hits the first enemy. It's on a timer before it explodes, and I guess if it hits the ground it won't explode. Back up first, you'll eventually get a feel for how far it travels before it explodes and how it moves through enemies. Trust me, the damage from the explosion is worth it. Unfortunately it seems distance is just outside of Flame Jet range.
4.) Smoke Vent is actually great damage migitation, an underused skill. Useful when under heavy attack.
Honnestly whatever you want as long as it doesn't cause you to let go of your Flamethrower. Supply drop is nice for the stun and utility it provides, but if you have a racial elite you like better then go with that.
Let's break it down by category:
Firearms (30): All that beautiful condition damage. Having Precise Sights set is just extra, the other trait options don't really fit with this build. With Elixir B it'll proc an ok amount, especially since the Flamethrower is a fast attacking weapon. You might consider switching it out for Infused Precision, too. Fireforged Trigger is a given, and is just delicious. The new updates to Juggernaut make this build unstoppable.
Explosives (10): Took me a bit to decide on this, but after noticing how much this build procs crits, decided to use Explosives' Incendiary Powder trait. Flame jet only procs burn for 1 second at the END, but wouldn't you just love to see your enemies catch fire more often and for longer? I know I would. Placing a bomb upon dodging is just extra fun.
Alchemy (30): Free Elixir B? Hell yes. Fast Acting Elixirs is an excelent option for slot one, and you absolutely must have Deadly Mixture in slot two. Energy Conversion Matrix makes Elixir B all the more sweeter.
From 11-39 just try to keep an even spread between Explosives, Firearms, and Alchemy, prioritizing Alchemy until it's capped, then Firearms, then Explosives. At 40 you get the next tier of traits and a bonus respec, so when you do, immediately cap Alchemy, then put 10 in Firearms. From there, follow this pattern:
40: E.0 F.10 A.20
45: E.0 F.15 A.20
50: E.0 F.20 A.20
55: E.5 F.20 A.20
60: E.10 F.20 A.20
65: E.10 F.25 A.20
70: E.10 F.25 A.25
75: E.10 F.30 A.25
80: E.10 F.30 A.30
So, enjoy this build! You're going to have a lot of fun!