i created this build because i think that the pillar of flamme is the best AoE skill of brand.
most of the other builds i saw used conflagration as the main damage source. When the target is ablaze pillar of flamme deal 25/100 more damage while conflagration only spread to nearby target.

Pros

good AoE damage
good survivability(with good item)
epic burst combo

Cons

low mana
alot of cooldown
usually the one who get focused in team fight(because of high AoE damage)

Greater Mark of Magic Penetration:combined with sorcerers shoes and void staff give good magic penetration.
Greater Seal of Scaling Mana Regeneration:brand don't have alot of mana so some mana regen is always usefull.
Greater Glyph of Scaling Ability Power:give some ability power.
Greater Quintessence of Ability Power: ability power

Sorcerer's shoes: give mouvement+ good magic penetration

Rylai's crystal scepter: ok. i take this item because A)it give good ap B)good health and survivalitity C) some slow. I take early game for the survivability and because i hate to be squishy

Rabadon's Deathcap:don't need any explication

morello's evilMorello's evil tome: Give ability power but more important: give cooldown reduction. Brand got alot of cooldown so getting CDR is essential.

Lich bane: give good ap and mana wich is really usefull with brand(note: if you got alot of mana problem change lich bane for archangel staff)

Void staff: good ap+magic penetration. feel free to change this item if you don't need mana penetration

Will of the ancients : if you gotm a team with alot of ap champ will of the ancient can be usefull

Archangel's staff: if you need mana it's the perfect item for you. Also it give alot of ability power with time.

Abyssal scepter: good ability power+ magic resist and the most important thing: it reduces magic resistance of nearby unit wich is really usefull in team fight.

Frozen heart: if you need some armor and maybe mana you can buy this item even if i don't reccomend it.

no need to explain masteries

i max pillar of flamme first because it's one of brand best ability. it give alot of AoE damage and you won't waste mana even if you do it on a single target.

after i take Conflagration because it can do great damage and can also do AoE damage on ablazed target.

finnaly i max Sear. i max it late game caue it is not the greatest damage ability. i still take 1 rank early game to be able to stun.

standart 1v1 fight
Conflagration--- Sear--- pillar of flamme
team fight
Sear--- Conflagration--- pillar of flamme--- Pyroclasm
burst combo
Conflagration--- Sear--- pillar of flamme--- Pyroclasm

you can aslo use the team fight combo to farm minion.

normal summoner spell

flash: good escape and gank spell. always usefull for a mage

Ignite: combined with you blaze your target will not be able to survive after a fight

good summoner spell

Ghost you can change Flash by ghost even if i prefer flash due to the fact you can flash trough wall

Clarity this is a good spell for mana problem

Teleport this is a good spell if you are about to solo mid.