My Stats:

-Mini-crits cause afterburn for 3 seconds.
+Afterburn Damage: 4

-Random Criticals are Mini-crits.
-Mini-Crits do no additional Bullet Damage.

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Additional Notes:

Can be used with Crit-a-Cola.
Targets have to take a minimum of 20 bullet damage to be set on fire. (To avoid setting large groups on fire at long range.)

Hmmm, I have these thought up
+On hit, Afterburn. Lasts longer if more shells hit
+Random Crits/Kritzkrieg grants Mini-crit afterburn
-25% Larger spread.
-On miss, Ignites you for 6 seconds.

Stats:
+ 20% damage on burning enemys
+ 30% fire damage resistance on wearer
+ crits against burning foes
- no random critical hits
- 20% damage penalty against non-burning foes
- 37% smaller clip size (4 bullets instead of 6)

I like Dystopius's stats. Nice and simple

on hit ignites enimies dealing afterburn damage for 3 seconds
afterburn damage persecond 5

-34% CLIPSIZE
+ 35% fireresistance
minicrits burning players
take minicrits if on fire
-25% firerate
+ 25% reload speed

I think just Cons:
-50% Clip Size
-20% Damage
And for Pros:
Alt fire charges up (about as fast as flying guilitine but a little slower) and on alt fire you do an airblast type thing (but has to re-charge when used)
and sets enemies on fire for 5- seconds (after burn for 5 seconds at long range, 6 at medium and 7 seconds at close range and 8 for point blank and critical hits)
(does not give you super long after burn if using crit-a-cola)

+30% Movement speed
+Critical hit on burning players
-66% Clip size
-25% Attack speed
-No random critical hit

some stats for fun:

pros:
15% ignition chance on shot
10% reload speed
5% firing speed

cons:
-30% clip size
-5% damage to players

and maybe the strange scorched shot could count kills with people on fire or pyro kills or something like that.

Minicrit-Crit
Crit-Minicrit
And -50%clip size

I think it should be kinda like the backscatter

Pros:
+Ignites enemy if shot up close
+Can ignite huntsman arrows
+mini-crits burning enemies from behind
Cons:
-30% damage
-33% clip
-no random critical hits
-15 health

Pros:
After burn on hit
Cons:
-10% damage
-33% clip size
-25% primary ammo

My stats
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+burns enemy for 5 seconds 4 damage each second
+20% fire resistance
+makes a fire ring around you when you shoot
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-fire does 2 more damage on you
-no random crits
-on pyro's less damage

Pros

25% fire risitance

enemys on fire does 100% critical hit

10+ health

Cons:

-30% ristance to explosions

no random critical hits

-20% ammo

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also change the name, some people might get confused about the name because theres a pyro flare gun called the scorched shot maybe call it "The 100 degree blaster" or "The Hell Barrel".
Also the craft should be 1 blackburner, 1 back blaster and 1 reclaimed metal.
this is just an idea.
Thanks for reading.

-20% damage
no random crits
on hit: 5 second afterburn

this would make the sun on a stick less useless