Personally, I feel that something like this deserves some of the stas that he gave it, but it needs a definite downside: Airblasting someone to mark them for death is incredibly broken, even if the flames only do damage when that effect is there. Remove that whole "mark for death" thing, and make the range of this weapon extremely small. I also recommend the damage bonus to be 10% instead of 25%, or at least something lower: As for the afterburn, it should last ~10% longer, but not do more damage.
The DOWNSIDE should be something range related: There hasn't been a single flamethrower to date that has had a smaller hitbox and less range on the actual flames. It would be nice to see something like that in the game, and it would surely encourage a different style of play where you would have to get even farther into someone's face than usual to deal damage. Adding on to that, a weaker airblast is a trait we've never seen, either: Put the two together and you have a high damage but high risk monster.
To recap:

+10% damage
+~10% longer afterburn (probably less, it feels more balanced)
-Has a smaller hitbox, and the flames don't stretch as far
-Airblasts send the target a quarter as far compared to other flame throwers (this is up for debate as well).

What do you guys think?

Here’s my suggestion for stats, perfect for what the Pyro is unmatched in; hit and runs:

+ Afterburn deals 2% of target’s current max health as damage per half second
+ Airblast is constant stream as primary fire is but at twice rate of ammo cost
- -50% damage penalty

Here’s a graph to show the first mechanic, keeping in mind that all damage in TF2 is rounded up

Current Max Health of Ignited Enemy (h) ---- Afterburn Damage per Half Second for 10 seconds

50 < h ≤ 100 ------------------------------------------- 2
100 < h ≤ 150 ------------------------------------------ 3
150 < h ≤ 200 ------------------------------------------ 4
200 < h ≤ 250 ------------------------------------------ 5
250 < h ≤ 300 ------------------------------------------ 6

+Flames stay in air for 1.2 second before fizzling
+Airblasts move airborne flames
+Mini-crits when flames are pushed into opponents
-70% afterburn time
-20% default damage
-Airblasts don't affect players or projectiles

+25% more damage to spies
+10% more damage to all other classes
+10% movement speed
-No airblast
-5 seconds afterburn duration
-25 max health

Cons:
10%less damage
afterburn is 3 second shorter
pressing 'R' (deafult) will change its alt-fire: airblast (10% more expensive) bleeding or soaking in jarate. Each 'airblast' except funnily enough airblast will cost 50 fuel. i think that this could pull out some interesting combos but may be too OP.
new taunt:
pyro pulls out a grenade and puts it on the ground, he then lines up his shot and hits it like a golf ball with the tiki torch, it would have the explosion radius of a rocket and afterburn but you have a chance of missing and blowing up yourself (idiot)

I know I'm a little late on this, but from the looks of it I think it should inflict a kind of 'Cursed' effect instead of afterburn.

Fire victims will receive a 'Cursed' effect instead of receiving afterburn that will last for 10 seconds
(+) Cursed victims will take extra damage from teammate attacks depending on how much damage you did with your flame, up to 50% extra damage.
(+) Cursed victims move 10% slower (This slowness effect isn't as strong on slower classes)
(+) Curse cannot be removed by healing sources
(-) Curse will deal no damage
(-) Extra damage effect will be halved for damage dealt by your other weapons
(-) Flame will initially deal 1 damage per particle
(-) Longer airblast refire time maybe? (meaning it'll take longer before you're able to airblast again)
Counteracting the effect above, the damage will increase up to 4 damage per particle

and now for something completely diffrent... LAVA!

whaaaaat, you heard it. tikis, valcanos....??? well heres the stats

+can spray lava on the floor that lasts (5?) seconds
+anyone standing in lava will be slowed.
(when in lava its like being blasted in the face with the defualt flamethrower)

-30% slower fire/projectile
-can only be sprayed on the floor, not directly at enimies like the defualt flamethrower,

=Damage builds a "summonings" meter, the max amount damage that the meter can hold is 500
+When meter is 25% full, grant a speed bonus to the user for 2 seconds
+When meter is 50% full, grant a speed bonus and a 25% damage resistance to the user for 4 seconds
+When meter is 75% full, grant a speed bonus and a 50% damage resistance to the user for 6 seconds
+Summon an aztec elder god for 8 seconds when the meter is full (HHH reskin)
+50% larger flame size
-45% damage penalty

primary- disconnects you from server
mouse 2- changes to a better class