Is a breath weapon a natural attack in Pathfinder? I'm trying to build a class and want to increase the damage it deals with the improved natural attack feat.
Breath weapons are not natural attacks.
If you refer to the universal monster rules, you can see that Breath Weapons and Natural Attacks are listed separately; though the description of natural attacks does only include the "most common" kinds of natural attack as examples and allows for other options, breath weapons are separately described as their own special feature, and are not a natural attack form unless explicitly clarified so (though I'm not aware of any monster or ability which does).
I'm don't think there are any first-party options/feats/etc. which increase breath weapon damage, but you could always take Ability Focus with your breath weapon to at least make it harder to avoid.