Brayflox is the first real test of any player in this game and thus players will be required to step up and face the challenge. One of the important skills a WHM should learn is the ability to manage their MP and understanding the dynamics of a fight so they know when to heal and it shows in this dungeon.

General things to know about healing
  • How much you can heal for - This allows you to gauge approximately how much collateral healing you'll need to do on non-tank targets to keep them alive through the next barrage of attacks. While it would be great to keep everyone at full HP, sometimes it's not possible and your priority should be the tank and keeping the non-tank roles alive just enough for them to survive a random hit (This also becomes infinitely easier once you have Regen)
  • How a fight pans out - This can only be achieve with experience. XIV is a heavily scripted so after you do a fight enough, you can generally predict when these attacks are going to occur and thus be able to heal accordingly.

Aiatar has three primary attacks of concern for a healer:
  • A frontal line attack that adds a stack of poison and does heavy damage if the tank gets clipped (this is unfortunately something out of your control and will need to respond appropriately if the tank DOES get clipped)
  • A toxic spit that gives the target and anyone else hit a poison stack and deals damage - leaves an environmental hazard on the ground that no one should stand on (including Aiatar, as he regenerates HP while in these pools)
  • A normal attack that gives the target (should be the tank) an additional stack of poison

As a WHM for the fight, your goals should be as follows:
  • Remove Poison stacks via Esuna at the earliest and safest moments of the fight (a time where the tank is sufficiently healed so they may not die to the next attack)
  • Removing Poison stacks from DPS hit by the toxic spit and giving them enough healing to survive the next toxic spit if they are targeted
  • Positioning far enough away from Aiatar (and if possible, towards a wall) so you can heal effectively and reducing the amount of coverage a pool may have on the arena

This is what a healer can do to minimize the risks of a fight from a healer's perspective. Unfortunately, there, you may need to carry more or less depending on the competency of your tank and how many melee DPS you have, as more melee DPS means more Aiatar repositioning due to Poison spit. Base your decisions on party competency and composition and you'll be able to get through it.

One general word of advice for gearing - I noticed through your Lodestone that you have a Danburite Earring equipped. Intelligence does nothing for your heals, so if you can replace that with a Mind earring as soon as possible, it would give you a small boost to your heals. If you have any friendly FC crafters, I'd ask them to see if they can make you a free set of HQ Malachite Accessories to help out.

Otherwise, your gear looks to be in relatively good shape. I would recommend running Brayflox a few more times to (1) get a better feel for healing as you'll really be put to the test once you hit Stone Vigil and (2) the Battlemage set is good enough to last until you can get to the first set of AF gear at level 45, so I recommend getting a full Battlemage set if possible.

Happy healing!