Burning Spell +2 spell level
Benefit: The acid or fire effects of the affected spell adhere to the creature, causing more damage the next round. When a creature takes acid or fire damage from the affected spell, that creature takes damage equal to 2x the spell’s actual level at the start of its next turn. The damage is acid or fire, as determined by the spell’s descriptor. If a burning spell has both the fire and acid descriptor, the caster chooses what kind of damage is dealt by the burning spell effect.
Acid Arrow Spell level 2
An arrow of acid springs from your hand and speeds to its target. You must succeed on a ranged touch attack to hit your target. The arrow deals 2d4 points of acid damage with no splash damage. For every three caster levels you possess, the acid, unless neutralized, lasts for another round (to a maximum of 6 additional rounds at 18th level), dealing another 2d4 points of damage in each round.
Say the spell is cast at caster level 7, which allows acid arrow to take effect for 3 rounds. The round it hits it does 2d4. The second round is 2d4 + 4 from burning spell. Now does the spell only do 2d4 or 2d4+4 on the 3rd round? Does it deal another 4 on the 4th round since the spell would have finished but the wording of the feat suggests it lingers?