So, this started as a desire for a gnome barbarian (for obvious reasons) - then the thought of the bloodrager came up, and that sounded even more fun, given the inherent magic nature of gnomes - so then the obvious connection was a pyromaniac Gnome, with an elemental fire bloodline bloodrager.
Gnomes with this racial trait are treated as one level higher when casting spells with the fire descriptor, using granted powers of the Fire domain, using the bloodline powers of the fire elemental bloodline or the revelations of the oracle's flame mystery, and determining the damage of alchemist bombs that deal fire damage (this ability does not give gnomes early access to level-based powers; it only affects the powers they could use without this ability). Gnomes with Charisma scores of 11 or higher also gain the following spell-like abilities: 1/day—dancing lights, flare, prestidigitation, produce flame. The caster level for these effects is equal to the gnome's level; the DCs are Charisma-based. This racial trait replaces gnome magic and illusion resistance.
Here's the thing though. The Bloodrager's elemental abilities, in theory, gain benefit from Pyromaniac (which says it affects bloodline powers) - however, none of the abilities are in any way level dependant. Except 'possibly' this:
At 1st level, three times a day as a swift action you can imbue your melee attacks with elemental energy. For 1 round, your melee attacks deal 1d6 points of additional damage of your energy type. At 8th level, you can use this ability up to five times per day. At 20th level, all your melee attacks deal this damage, and this ability no longer requires a swift action to activate.
Now, the Gnome ability makes this ability function 'as one level higher'. but it also states that it 'does not give gnomes early access to level-based powers'. So, is the 8th & 20th level progression of this ability a level dependant effect, or the granting of a new 'level-based power'?
An additional question. The Gnome Bloodrager FCB does sort of the same thing.
Add 1/4 to the bloodrager's effective class level when determining the power of her bloodrager bloodline powers.
So does this have any effect on an elemental bloodrager?
The FCB almost certainly does, and I can't see any reason why the racial trait wouldn't either. As you've noted, all it does it get you access to a few more rounds of flaming weapons, and not that early.
So, in that vain, the FCB doesn't have the blurb about not granting the ability early. Does that imply that for every 4 levels of FCB, it bumps up Bloodline progression by 1 levels?
Well, pyromaniac only affects class levels for purposes of detemining the effect of class powers.
But the FCB... I do really think it only adds the bonus in the same way, as it says "when determining the power of the br bloodline powers"
Unfortunately, that's how I would interpret it as well - however, with that interpretation, it is hands down the single worst FCB in the game. If interpreted that they only affect 'per level' effects of bloodrager powers, and not when those powers are gained or improved, then this is the entire net benefit of each FCB taken for all published Bloodlines. This really hurts to look at with that interpretation:
Aberrant - Staggering Strike (1st) - extra 1/8 to DC per FCBAbyssal - No effect at all
Arcane - Caster's Bane (20th) - casters 1/4 level per FCB lower trigger AoO always
Black Blood - Retributive Spray - extra 1/8 to DC per FCB, extra 1/8 Damage per FCB
Celestial - No effect at all
Destined - Destined Strike (1st) - extra 1/4 to hit per FCB
Draconic - Breath Weapon (8th) - extra 1/8 to DC per FCB, extra 1/4 of a d6 to damage per FCB
Elemental - No effect at all
Fey - Confusing Critical (1st) - extra 1/8 to DC per FCB
Infernal - No effect at all
Kyton - Painful Strike (1st) - extra 1/8 round duration per FCB
Kyton - Unnerving Gaze (16th) - extra 1/8 to DC per FCB
Undead - Frightful Charger - extra 1/8 to DC per FCB