Beefed this up a bit; I'm hoping this will do as well as a single Quest deck, if not better.

I should have thought of this before: Proliferate!
Specifically: Volt Charge!


So I came up with this.
"Dual Quest"
Which throws in Keldon Marauders. It guarantees 2 triggers (or more) on Quest for Pure Flame for only 2 mana.

One Volt Charge can add a counter to both enchanments and the marauders to keep it around longer (something opponents would probably never see coming :D ).
Unfortunately, these two Quests are at odds with eachother. This version doesn't even have room for the Guttersnipe staple!




Focusing on Pyromancer Ascension, I came up with "Pyromancer Battery".
It utilizes Faithless Looting to outstanding effect. Using it to bury a Volt Charge in the graveyard, casting 1 Volt Charge alone will activate Pyromancer Ascension. It's also great for getting rid of unnecessary cards (duplicate enchantments, excess land), or getting more land if you don't have enough, and effectively drawing extra cards with Flashback and Madness.




Both decks seem like they're very fun, but still a little clunky (getting that balance with red is pretty hard). So, focusing on easier-to-activate Quest for Pure Flame, I made
"Like Finding a Needle in a Bonfire" [cheesey name based on Quest for Pure Flame and Needle Drop]
This deck has less staying power than the other 2, but makes up for it in speed. It can win on turn 4 - via multiple ways. Did it once even after taking a mulligan down to 5 cards. It also has the luxury of not being shoe-horned into playsets of every card by Pyromancer Ascension.


Out of 13 self-plays, it had this many wins on each respective turn:
Turn 4: 3 (23%)
Turn 5: 4 (31%)
Turn 6: 6 (46%)


[For the playtests, I assumed the following. Handicaps: Keldon Marauders does not hit opponent. Did not draw card on first turn. Pros: Opponent did not heal. No spells countered. Other: Guttersnipe dies after 2 turns.]




So that's what I've got! Feel free to take 'em or edit them as you please. Cutting it down wasn't that easy, as all these cards are good, but each cut has its reason. I'll happily answer any questions.

[/For the playtests, I assumed the following. Handicaps: Keldon Marauders does not hit opponent. Did not draw card on first turn. Pros: Opponent did not heal. No spells countered. Other: Guttersnipe dies after 2 turns.][/cheesey name based on Quest for Pure Flame and Needle Drop]

This looks pretty good and fun.
I'd ditch the Spark Elementals. At best they're a 3 mana burn spell that doesn't work with your Guttersnipe, Pyromancer Ascension, Past in Flames, or Increasing Vengeave. At worst it's worthless.
Take a look at these one drop spells instead:
Dead // Gone (shock // unsummon)
Burst Lightning (good early or late)
Firebolt (good early and late)
Needledrop (But this one you won't cast turn 1. You must already do damage to cast it, but it nets you a card. With Pyromancer Ascension ready you get 2 damage and 2 cards for 1 mana!)


And one more card I'll point out: Staggershock
This card + guttersnipe will put 4 quest counters on Quest for Pure Flame all by itself. You cast it once for 3 mana, and it does a measely 2 damage (instant speed though). Guttersnipe will net your 2 more. Then it's cast again for free the next turn! 4 more damage! Heck, it still even goes into your graveyard after it's all done.


And none of them cost more than a quarter!

Fyi, you do know you have to sac quest to activate the double damage, and only for that turn, right?

Put Past in Flames back in, removed all Bond of Agony. Really want to change back to Lava Spike, only because it would benefit from Quest for Pure Flame as well; but it's expensive and has no inherent Flashback (though that is oft too late in the game anyway).

Added 3x Bond of Agony, removed most spells over 2 mana.

try adding goblin guide's and terminate's (for kill) - perhaps sideboard.  if detonate is modern add that for artifact kill

I'm debating taking out Painful Quandary and adding Chandra's Phoenix.

After 10 or so one-sided playtests, I was getting to lethal damage by turn 5, latest 8. Ran into mana starvation once, but lightning bolts / unearths held me over. 
I did notice, even with just 2 of the Grim Lavamancer, I was having trouble powering the ability with my graveyard. I was often pulling these in the first hand or early game, and especially with flashback/unearth, I was very reluctant to activate it even during the short times I had the option to. Exiling my own cards may just not be my style (at least not the deck's), even though it is an awful nice trade.
To be honest, Grim Lavamancer would do great in my Goblin deck.

what is your budget for the deck?

So made a few more changes, added a playset of Anathemancer, replacing 3 Ball Lightnings. Took those out due to price* and potentially easy to remove. I prefer the instant effect of the Anathemancers, and it is very true everyone is running plenty of nonbasic lands.
I will be closely studying the feasibility of reusing the graveyard and punishing the opponent for it versus eating the graveyard ad punishing the opponent for it :P
Also added 1 more Browbeat, because it really is a beautiful soft burn.
Card total is at 62, can't decide on the trim.

With over half your lands turning on dragonskull summit, the shocks are not necessary.
Suggestions:
-4 Gutter Snipe (Too slow)
+2 Grim Lavamancer
+1 Browbeat
Swap Incinerates and skullcracks (this would be a meta call)
+1 Anathemancer
(finding more space for anathemancer might be awesome, if you face people using non-basics alot. which you will)


Sideboard stuff... I don't see the point in anything you've got on there (assuming my suggestion of swapping incenerate/skullcrack). Your sideboard will be to deal with other decks you face that use a difficult mechanic. Without knowing your meta, that's hard to predict. Slaughter Games is probably a good choice. Its expensive, but un-counterable and can shut something down in a heartbeat. Make sure you don't give free info on it. You don't have to name the card until it *resolves*, meaning its too late for them to cast the named card. Lots of people don't know that :) 


You need some way to deal with artifacts, I'd recommend rakdos charm. That'll blow up a cranial plating, which is a real threat. 
Life's finale too slow, you shouldn't need to board wipe, and if you do it's too late on turn 6 in modern. 
Combusts might be a good idea in your sideboard for blue decks. Plus, don't forget to use triggers right. If someone flashes something in to block, you can respond to their enter-battlefield trigger and burn it *before* they can declare blocks. They still get the ETB effect, but they dont block your generic dude.

I mainly put in Lava Spike for it's cheap R cost and in conjuction with Past in Flames/Lightning Bolts: deadly. Bump in the Night (don't remember taking that great burn out), I'll probably put pack in, but I don't want to see Lava Spike go.. And you are very right about the shocks.. probably should just let them sit out for now.

Agreed, Browbeat would do much better here, I'll change that straightaway.  I modified the lands, mostly following your suggestions, hate to see the Akoum's go, but I see this deck needs the mana before the +1 life. Sideboard needs lots of work..

If you're concerned about cost, remove the blood crypt's, in burn dual lands are really unnecessary when you can do dragonskull summit.  Also - bump in the night is better than lava spike in every way (since nothing is spliced onto the arcane)  same cost but has flashback
and is monetarily cheaper.

Instead of running diabolic tutor, run Browbeat.

Not bad, but I'd look at your landbase. Burn can't afford to have their lands coming into play tapped all the time. The Lavaclaws are reasonable. Ghitu is not good enough, nor is Akoum Refuge. 2/2 Bloodcrypt / Dragonskull would be better. Obviously replace the crappy non-basics with basics
Incinerate is better than annihilating fire, period. 

Made a lot of edits, then re-edits to get the price (way) down. Hopefully more lethal now ;)

This: http://deckbox.org/sets/336554
Is a competative level B/R burn.

As a competitive deck i see you going 1-3 at a tournament, maybe 2-2.  I don't see this as a competitive modern deck.