I already know how the archtype works. The best cards in the archtypes are by far Cerberus and Griffin because of how easy they are to splash. The deck is at its maximum potential with Fire King or Fire Fist.
Here are a few things you first need to understand to be able to start kicking some ass:
About traps:
You first used
Trap Jammer in your deck then settled in with
Mystical Space Typhoon who is a better choice. You actually did quite well to not use
Dark Bribe.
Dark Bribe is considered to be a bad card because if you use negate a card with this card. You'll use one card to disable another card. In other words: 0 card advantages. However after that, the opponent can draw because of
Dark Bribe effect. It means that
Dark Bribe is a -1 card advantage and that's why it's the worst choice you can take when it comes to spell/trap negation. The best trap cards for traps are:
Trap Stun,
Royal Decree,
Dust Tornado and
Seven Tools of the Bandit.
Obviously,
Mystical Space Typhoon is a much better choice as it can be used at any point.
However, if you want to be competitive,
you have to look closely at the actual metagame: Dragon Rulers, Prophecy and Evilswarms.
Dragon Rulers and Prophecy represent something like 80% of the format. And none use traps.
If you end up going in a tournament, you have 4/5 chances of ending with
MST or
Heavy Storm being useless.
Yes, that's the reason why people consider
Heavy Storm and
MST to be bad cards this format. That's why I end up rather siding 3
MST in all my competitive decks. Same thing for Huge Rev and Starlight Road. If no competitive players use those cards anymore, those cards aren't really useful.
Now if you look at your main deck, you'll notice something rather important: You don't have any removal anymore. In fact the only removal you had consisted of spell/trap removals.
There is a rather important card that you overlooked though because it was level 7:
Blaster, Dragon Ruler of Infernos.

The reason why you ABSOLUTELY need that card in your deck is because of his secondary effect: discarding another fire monster to destroy one card on the field.
Not only will it allow you to keep going with field control but you can also recycle it. If you use his effect from the grave to summon him, you'll have a 2800 ATK beater on the field (Meaning you need 5200 ATK to OTK if you just have him in the grave). Usually, your opponent won't try to beat it as it will go back to your hand during his end phase. But that's actually what you want. Letting it go back to your hand allow you to use his removal effect next turn.
Adding
Burner allow to boost your consistency and the chances to get
Blaster ASAP.
Banishing monsters also allow you to maximize
Laval Lancelord's effect. You can also improve the little guy even further with
Circle of the Fire Kings and/or
Fire King Garunix. Don't forget that with a
Blaster in the grave,
Return from the Different Dimension is overkill in that deck.
Rekindling is only good if your deck rely on it and it's far from being that good in that deck. If you want to play
Rekindling, play Hazy Beast/Fire King otherwise ditch it. Even in that deck though,
Rekindling is considered to be meh and kill consistency.
Molten Transmission and
Laval Volcano is a huge waste of deck slots too. You either play pure
Laval or you don't play them.
Anyway, I ended up writing a lot but I suggest you to take a close look at either
Fire Fist or
Fire King. Getting for example
Tenki,
Fire Fist Gorilla and
Bear will allow you to get tremendous removals while allowing to not hurt your
Hazy Beast combos. Get one not both at the same time though.
Like you can see, your deck got a lot of potential but getting the right balance will take a lot of time. You can be proud of you if you end up with something good though.
If you need more insights, I'll give more advices but be careful to not mix helping and spoonfeeding.
PS: For side-decking,
we got a thread made only for that .
And remove
Norito, you added the anime version who requires 2 lvl 6 monsters when the real version requires 2 level 6 spellcasters.