First item is that I think you may be confused as to what Book Burning does. The current Oracle text of the card (they changed the card text about 5 years ago because the printed version is confusing) is:
Any player may have Book Burning deal 6 damage to him or her. If no one does, put the top six cards of target player's library into his or her graveyard.
This means that you don't get both the damage AND the mill... you get whichever one your opponent chooses. Your opponent will ALWAYS choose to mill 7 cards instead of take damage. That's why the card is bad in a burn deck... you never deal damage with it.
There are a lot of burn spells which are significantly better than what you're currently playing. One of the philosophies of Magic that you have to get used to is that your life total is a resource. It does not matter if you are at 1 life or 1000 life... as long as your opponent has 0. You are free to take damage (even from your own cards), if it furthers your goal of bringing the opponent from 20 to 0 as quickly as possible. To do this, you want to play the fastest, most efficient burn spells possible (the average mana cost of the cards in my suggested deck is 1.2, in yours 3.5). On average, you won't be able to play anything until turns 3-4 given your average mana cost... while I will have completely emptied my hand and won the game by turn 4.
I've included relative prices for you, per card.
Lightning Bolt ($3) - 3 damage for 1 mana instant. Can't beat that.
Lava Spike ($0.10) - 3 damage for 1 mana sorcery. Still pretty good.
Chain Lightning ($7) - Same as Lava Spike.
Flame Rift ($0.25) - 4 damage to everybody for 2 mana. You taking the damage doesn't matter... as long as they do.
Flamebreak ($2) - 3 damage to all creatures and players for 3 mana. Better than Pyroclasm b/c it hits more stuff and gets your opponent.
Fireblast ($2) - The mac daddy of burn. 4 damage for the low, low cost of sacrificing 2 mountains. You can even pay 4RR if you have to... Best burn spell ever printed!!
Mogg Fanatic ($1) - Yes, it's a 1/1 creature for 1... but it usually winds up hitting the opponent for 3-4 damage per game. Attack early, and when it's no longer useful, sac it to hit your opponent for another 1.
Grim Lavamancer ($6) - Another 1/1 creature... with a really good ability. Why not let your burn spells pull double duty as extra damage. All you have to do is pay R, tap the Lavamancer, and remove 2 cards from your graveyard to deal 2 damage.
Price of Progress ($1-2) - If your opponent plays a lot of nonbasic lands, this is devastating. It deals 2 damage for each nonbasic land in play to whoever controls it. Since you only have Mountains, you aren't affected... but those decks with dual lands easily wind up taking 8-10 damage off this 1 spell for the price of 2 mana. In Eternal formats, if this card resolves... you usually win.
Ball Lightning ($8) - a 6/1 trample haste for 3 mana. It's ok, but it's huge drawback is that it's got a bullseye painted on it and gets killed before attacking most of the time.
Barbarian Ring ($1-2) - A land that can tap for red (at the cost of 1 life). When you get 7 or more cards in your graveyard, you can pay a red, tap and sacrifice Ring to deal 2 damage (which is colorless) to a target. I know some people who swear by this card, so I'm giving it to you as an option.
Wooded Foothills ($10) and Bloodstained Mire ($9) - You pay a life and sacrifice them to go find a mountain. You're probably asking why include it instead of basic lands?? Here's why:
1. You can find dual lands (Taiga, Stomping Grounds etc) with these, if you ever want to splash a color.
2. It thins your deck of extra land... this means that you draw more burn spells.
3. If you have Lavamancer, these cards are an automatic 1 damage to the opponent.
Incinerate is good.
Here is what I would recommend, if your budget allows:
Creatures-
4x Mogg Fanatic
4x Grim Lavamancer
Spells-
4x Lightning Bolt
4x Chain Lightning
4x Lava Spike
4x Incinerate
4x Flame Rift
4x Fireblast
4x Flamebreak
4x Open spots for what you like
Land -
4x Bloodstained Mire
4x Wooded Foothills
12x Mountain
Sideboard-
3x Shattering Spree (replicate copies aren't played, so it won't trigger chalice of the void set at 1.. which happens to neuter your deck)
4x Pyrostatic Pillar (for combo decks relying on cheap spells. taking 2 to deal 3 isn't a bad tradeoff)
3x Earthquake (extra board sweep which hits the opponent)
3x Sulfuric Vortex (for control decks, or decks with life gain)
2x Relic of Progenitus (for graveyard recursion decks)