Hello Guys,
Im Misterfirstblood from EUW.
I want to show you my "maximal Damage" Guide on Brand.
At first i have to say that my English is not the best because im from German & this is my first Guide.

I begin with the Summoner Spells.
I prefer to take Flash and Ignite.

Flash because Brand has no escape Potential and Ignite to finish up enemys/ reduce healing.
Smite / Revive / Teleport / CV Isnt very useful for Brand.
If you think Exhaust is a better Tool to finish up enemys you can try it.
Barrier is an option too if you play against enemys with a hard skill combo damage like veigar.

Now the Items:
In my opinion Brand is only good for dealing Damage and kill enemys damage Dealers easy.
To play him very tanky isnt a good choice because the Cooldowns are "too high" to cast more than 2 Skillcombos in a fight. Because Brand is one of the AP Carries with 4 attack spells I prefer to play him for Maximal damage.
4 Skills, Ignite, Autoattacks, and the Passive. Your mid enemy will take Damage from 7 sources at level 6.

Because he is using many spells you should start with a Dorans, so you get Mana back if you lasthit Minions, what gives you more sustain.
The boots with magic penetration are very important for brand because they work very well on him.
If you have the boots, you should go for liandry's torment.
If you deal magic damage now, the enemy will take damage from your passive and from liandry's. Bot of this damage sources scales with enemys current health, so you can beat down Tanks easy too with this item.
If you have this core you have to go for the Deathfiregrasp. If you do a Combo with ult ignite and DSG first u increase the dmg from all of this sources by 20% what is insane.
With that 8 Damage sources you should get Lichbane too, if enemys chase you and u are on Cooldown you can hit them hard anyway.

If you get focused you better go a little bit more tanky, but if your positioning is good you should go for rabadon's and void staff.
Now buy the Blue elexir and you can beat down the enemies so fast.

For Runes take some Magic Penetration and AP Flat, Masteries the 21 Points for offensive are must have - Than you can skill 9 points to utility or tankynes.

The best way is to learn w first.
It is an AoE what is better if you get ganked and deals nearly the same damage like Q, and your hitrate is higher. So use Q only for the stun and engage with e ( w deals increased dmg if they burn, but get stunned too only if they burn so engage with e, stun, and press w ).
Than you should max your Q and E. ( Ulty SAP )

Now some tipps for the Gameplay:
- Play defensive to lvl 6
- Poke before you try to kill your enemy
- No Greed Flashes, you need this spell to escape
- Ward Side Bushes
- In Teamfights focus Damagedealers ( most effective )
- Ask for Ganks or jungle if you are losing

I hope you will try it and wonder about the extrem hard damage.

If i made some Misstakes in this text i hope you correct me ( i think so :D )

Hope you enjoy it.
Greetings from Germany