I've done Brayflox countless times since 2.0 and I've never had to use an antidote. The one that cures paralysis, whatever it's called, that one is helpful sometimes. But I've never had a bother with poison.

Now if we're talking about derps that stand in poisons, or tanks that can't avoid the breathe, that's a whole other issue and in those situations, white mages have an even worse issue on their hands. For one, they run out of MP much more quickly than they can spam Esuna. At least we have our little unlimited regen-ing device in a fairy.

Try the run several more times, make generous use of Adlo, energy drain and aetherflow. They work wonders.