Abilities
Blaze
Brand's Passive Blaze is what will do a lot of your damage in team fights, and give you that extra oomph in the laning phase. Blaze does a passive 3% max health damage per stack over 4 seconds.
Let's pretend the enemy has 1000 HP and 0 Magic Resist. If you have one stack of Blaze you will do 30 damage with smaller tick amounts of the duration (such as 8,7,8,7 - 7.5 damage per second). This stacks up to three times (15,15,15,15) however on the 3rd stack it will only stay on for two seconds (23,22) as the Blaze Explosion will trigger and reset the stacks to one. The 3% portion of this damage is nothing crazy HOWEVER, it will trigger slow effects from Rylai's Crystal Scepter from Liandry's Torment making it incredibly annoying for the enemy team as explosions will also give enemies one stack of Blaze if hit by a 3 stack explosion. As Blaze Explosion will also give one stack to nearby enemies, if they are clumped together mass enemy Blaze explosions will occur.
3 stack Blaze does progressively more damage with more AP and per level, it is common to do 20% max hp damage from around level 11.
Blaze also affects large monsters such a Blue Buff, Drake and Baron. This allows you to do a lot of damage to objectives.
Sear
Skill shot similar to Ezreal Mystic Shot. Will apply one Blaze stack and stun the target if Blaze is present on the target.
Landing this skill shot is the difference between securing a kill and dying, in some cases you want to be patient if your target has a Blaze stack as they will try and zig-zag and dodge your Sear. Remember you have 4 seconds until Blaze falls off, so if they are playing the dodging game, wait 2-3 seconds and throw the Sear during this time. You should be landing auto hits while they are running around doing no damage! Max level Sear after Pillar of Flame as it reduces the cool down per level by 0.5s.
You can start Sear as part of a damage combo, primarily used in lane. WARNING if used you are vulnerable as you will have no stun for the duration of the cooldown. ( Sear into Pillar of Flame into Conflagration)
You can also use Sear as part of a wave clear combo. Try and aim for the cannon minion first with 7 minions clumped around Brand. The combo is ( Sear into Conflagration into Pillar of Flame). However as support you will likely need to do another Pillar of Flame to clear the wave.
For more advanced users, you throw out Sear and while the projectile is still in the air, you can cast Conflagration which, if fast enough, will stun the enemy just before the Sear projectile lands.
Pillar of Flame
Pillar of Flame is your primary poke in the laning phase and the most damaging ability in your kit. It will do 25% more damage if Blaze is present on the target. It has a decent range, but the delay on the explosion is a tad slow. It is easiest to land this when the enemy ADC is about to last hit a minion.
You can use Pillar of Flame to start a stun combo ( Pillar of Flame into Sear into Conflagration).
Conflagration
Conflagration is an easy way for you to get one Blaze stack on the target and is primarily used to start a stun combo with Sear.
As of 10.22 Conflagration now is AoE without requiring a Blaze stack and the AoE range is increased if there is a Blaze stack. Use on a minion to apply 1 stack of Blaze on an enemy to easily apply the debuff to both the enemy ADC & Support.
Pyroclasm
Pyroclasm will bounce from Brand / Enemy champions / Minions and monsters. If you are lacking targets then use your own champion as a bounce source in order to increase the damage output of Pyroclasm
Pyroclasm will slow the enemy ONLY if they have a Blaze so doing a Conflagration beforehand is a good way for them to stop running away and preventing bounces.
Pyroclasm damage potential is greatly increased per level, (more so than most ultimates). Level 6 Pyroclasm gives you 100 damage per bounce with 30% slow if there is Blaze on, and at level 11 Pyroclasm damage is DOUBLED to a potential 1000 damage and 15% more slow. Getting to level 16 is not common as support unless it's a long game, but 1500 damage and the 60% slow is very nice.
In a few rare cases, I have used Pyroclasm to bluff it's a Sear. If you are at the same running straight angle and the enemy is flustered they will Flash thinking it's a Sear. This then enables you to Flash Sear and land a stun!