Burning spell metamagic

[Fleetwood Coupe de'Ville]

Burning spell:
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 2× 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. A burning spell uses up a slot two levels higher than the spell's actual level.

If used with a Flame blade spell, does the extra damage stack assuming multiple hits due to iterative attacks?

[Chess Pwn]

looks like it.

[Ravingdork]

I like it with things that do ongoing damage, like wall of fire.

[Azothath]

Burning Spell metamagic compared to Empower metamagic (standard choice). Caster Level(CL), Spell Level(SL).

It seems clear in the text of Burning Spell that "actual" means "original" spell level (see metamagic) or in combination with Heighten Spell, “effective” spell level. Thus a spell of SL does 2SL damage on the next turn without a save. Usually the save follows through with the damage type but here it seems to be the advantage of the feat if it takes any fire or acid damage from the initial spell effect.

For the sake of comparisons, I'm going to assume a competent spell caster at 5, 10, 15 CL with ability scores of 18, 20, 22 respectively and +0, +1, and +2 DC respectively from magic or feats.
Target base saves will be +1, +3, +5 respectively and +2, +4, +6 from magic and feats.

Fireball, SL=3: CLd6{10d6 maximum}[fire] Rflx DC 10+SL+Mod for dmg/2, AoE 20ft radius sphere at up to long range.
Burning: spell damage then 2*SL=6[fire], leads to respective averages of; 17.5@DC17 +6, 35@DC19 +6, 35@DC21 +6. After saves; 14.7 +6, 27.6 +6, 26.3 +6. (I use 0.8375, 0.7875, 0.75 to calculate after save damage on dice damage)
Empower at the same criteria would yield; 26.25@DC17, 52.5@DC18, 52.5@DC19. After saves; 22, 41.3, 39.4.
so Burning starts out a bit behind but significantly falls behind with CL as dice increase. Intensify would only increase the difference.

Burning Hands, SL1: CLd4{5d4 maximum}[fire] Rflx DC 10+SL+Mod for dmg/2, AoE 15ft cone. Burning will do 1d4*CL +2[fire] on the following round. Empower 1.5*(1d4*CL). After saves; Burning:10.5 +2, 9.8 +2, 9.4 +2 versus Empower: 15.7, 14.8, 14.1.
So again, even with a lowly 5d4 Empower is ahead.

Flame Blade, SL=2. 1d8+[CL/2 {maximum 10}][fire] {no STR damage, does not stack with weapons} with melee Atk. Up to 10*CL rnds (attempts with BAB and modifiers). Here due to caster level not affecting the dice of damage Burning will prove superior to Empower. After saves doing; 7.5 +4, 9.5 +4, 11.5 +4 verses 8.75, 11.75, 13.75 per hit.

Shocking Grasp with Reach and Intensify is still a better combo for single round damage via ranged touch attack and does not risk the caster being in combat.

So Burning Spell is only going to be effective with fire or acid spells that do not rely on dice, which generally have low damage. Energy Resistance is going to make it ineffective due to the low damage numbers.