There's a significant misprint in the Book of Demons: the summon spell for the Path of Flame lists the 5th level version of the spell as being able to summon forth a "Fire-Imp." But as you move on and get into the stat blocks for the actual demons summoned by the different iterations of "Summon Flame Demon," you see that this creature doesn't actually exist. Instead, at 5th level, you get an upjumped pallette-swap of the 1st level Burner.
For my campaign, I wanted to offer Flame Path Demonologists a bit more variety, and actually give them five distinct types of demons to summon. So, I cobbled together something of what I thought a Fire-Imp might be like in play.
Fire-Imp (5th level Spoiler [DEMON])
Initiative +10 (but will probably act on its summoner's turn)
Fire-Blackened Claws: +9 vs. AC – 6 damage, and 10 ongoing fire damage
Flaming Loogie: +9 vs. PD (1 nearby enemy) – 14 fire damage, and 7 ongoing fire damage
First Natural 16+ Flaming Loogie Roll Each Turn: The Imp can choose one of the following effects: either the target is Vulnerable instead of taking the ongoing damage, OR the Imp can make a Flaming Loogie attack against a different target as a free action.
Incendiary Curse Aura: Whenever a creature attacks the Fire-Imp and rolls a natural 1-5, that creature takes 2d6 fire damage. If any of these damage dice turn up a natural 6, the roll "explodes" and you can roll an extra d6 for more damage.
Flying: Fire-Imps have no problem flying, even though it looks like their wings are constantly on fire.
Degradation Mechanic: At the end of each of its turns, the summoned Fire-Imp loses 3d6 control points. (NOTE: If you don't use my modified Demonologist Summoning rules, then the Fire-Imp's hit points degrade instead)
HP 66 (56 for Flame Path Initiates)