RED QUICK BURN

It seems like with so many 1 and 2 mana spells you'll play out your hand really quickly. Maybe you'd benefit from some card draw. Faithless Looting will let you dump extra lands and works well with Guttersnipe or Young Pyromancer. If you want to throw in a couple of more expensive cards (manawise) in case a game goes long, I like Fire Servant and Galvanoth here.

Use kiln fiend for turn 3 win.

Take out Fire Servant. Add Pyromancer's Ascension.

If the idea is to burn the other player as fast as you can, maybe you could replace shock or searing spear for lava spike. More damage, one mana.

Here is my version of a burn deck, but it is meant for a group game instead of 1v1 you may be able to get some ideas.

http://www.mtgvault.com/melon57/decks/my-burn-deck/

Goblin guide

I have a burn deck using a similar gameplan to yours. I find that my deck loses to aggro if they are able to roll one out that's too big to shock/bolt to death. After that, a couple of enchantments or equipments on that one creature and I would lose the game. So in response to that, I throw in some Ensnaring Bridges and some Aether Flashes to keep the creatures at bay.

I'm on the fence about Melon57's idea of Elixir of Immortality. If a game lasts long enough that you need to do that, you probably already lost. Although 5 life is always nice.

Check out my burn deck if you want some ideas, I can win on turn 3 or 4 fairly easily

I dont think your creatures are fast enough. In fact, they are suboptimal for modern burn deck. Guttersnipe is 3-mana, just worth running in standard decks, in modern too slow. Fire Servant is fine in multiplayer or EDH, but 5-mana support for burn doesnt work. Goblin Arsonist is only good to sacing into Goblin Grenade, but even then its 2 cards and RR for 6 damage - thats the same power as 2 Lightning Bolts, but the Bolts are more reliable. Bloodcrazed Goblin is quite restrictive, you can't hold your instants to opponents turn (bad especially with skullcrack against lifegain decks). Goblin Guide is just better.
Ball Lightnings, Spark Elementals, Hellspark Elementals would do the job better. Or you can have approach similar to me: http://www.mtgvault.com/zipec/decks/br-burn-modern/

After i discovered storm every other red deck looks to me like its moving at snail speed. But you could easily add some nice cards, like Sulfuric Vortex, Goblin Guide or such the cards like Ball Lightning.

Fling could work good with this. Fling filn fiend after pumped or fling lightning ball after swing

how about arc trail, chandras spitfire and definitely inferno titan for late game, also in my opinion any burn that targets only a creature or only a player isn't what u want, leave your options open ;)

valakut, the molten pinnacle for lands

Simian Spirit Guide.

Now this mono red color deck is starting to look nice!!! Maybe use a Grim Lavamancer or 2

Glacial ray over skullcrack if you're running lava spike.