Quick Damage Red Deck

My suggestion would be to just Google "MTG RDW" or "MTG Red Deck Wins."  Odds are, it will give you a good sense of what a good build will look like.

Now, if I were to focus on this particular build, I see several issues:

1) Firedrinker Satyr is just plain bad.  I understand that all sorts of pros have been claiming it will be good, but consider the following scenario: The opponent is on the play, you put down the satyr on your first turn, they answer with a 3/3 (could be Kalonian Tusker, a Centaur Token, whatever).  On your second turn, you have the option to attack.  You swing, they opt to block.  You can easily make this a 1-for-1 trade, so you pay to pump the satyr.  Nice work, your 1-drop just took out their 3/3, and you traded, right?  Not so fast, not only have you lost tempo (kind of a big deal in RDW) by spending your mana to pump him, but you lose your creature AND you're out 4 life.  Alternately, which creature do you think they're going to zap with Lightning Strike?  If it's me I'll burn your guy and thank you for Forking my strike and letting me hit you with the copy.

So what's a better option?  Foundry Street Denizen and Rakdos Cackler are both solid options  that don't have the potential for getting blown out like the satyr.  Given that you have both of these, why bother with more one-drops?  You really don't want to be top-decking a one-drop beyond say the third turn.  As such, they should both be 4x, but you don't really need Legion Loyalist and the Satyr is just bad.

2) Burning-Tree Emissary definitely needs to be a 4x.  They're FREE 2/2s... How can that go wrong?

3) Firefist Striker is the optimal two-drop to accompany BTE, but for some nagging reason I think there should be at least one other option here... although I'm blanking at the moment.  Young Pyromancer seems to have found its way into several builds these days, although I think of it as being more of a control card.  Deathbellow Raider might actually not be terrible as an another two-drop.  Gore-House Chainwalker is probably the best bet.

4) Reckoner is a great creature, but not exactly the aggro piece you're looking for.  Definitely keep them in your SB for the mirror match, but I can see where a full playset of Chandra's Phoenix will serve you better at the three-drop.  In addition, Mindsparker or even Minotaur Skullcleaver is might be decent options here.

5) Purphoros is good, as is Chandra, but I would keep Fanatic of Mogis in mind as an added option at the four-spot.

6) I might would say to consider 2x Stormbreath Dragon as a finisher.  It's no Thundermaw Hellkite, but it's the best that we have for the time being.

For your spells:

1) You'll definitely want a copy of Mizzium Mortars (at least one MB).

2) Skullcrack really isn't necessary.  You could easily run one of the other creatures in their place.

A few other cards to consider:

1) Ash Zealot.  It might not fit the whole BTE plan, but a 2/2 with first strike and haste isn't exactly a bad thing.

2) Nykthos, Shrine to Nyx.  You're sitting on a TON of colored symbols and it's not unlikely that you have a BTE in play... you're going to be able to ramp using this.  Think, T1 - any one drop, T2 - BTE into Firefist, T3 - Nykthos, tap it for four - you're already landing Purphoros or Chandra.  If you manage the elusive BTE - BTE - Creature, now you're landing a Stormbreath Dragon on T3.

Anywhom, I'd suggest first looking into the RDW builds and then with any luck some of these ideas can be of use.