Edit: Answer received. The result is a fairly clear 'No, these two mechanics do not interact in regard to the Fire-based healing. Yes, they do interact on the Fire-based damage dealing.' on multiple grounds.
The post below has already been answered and is only retained in case others are curious.
I suspect this is a case where RAW never foresaw this possibility and so the RAW answer is 'No', but I want to ask anyway about how Healing Flames spell and Solar Bloodline arcana interact. Note that Healing Flames not being a Sorc spell is not a problem; Magaambyan Arcana trait can solve that.
Solar Sorcerer Bloodline Arcana:Whenever you cast a spell with the fire descriptor, if it deals damage, it deals +1 point of damage per die rolled.
Healing Flames: You unleash a blast of holy flames that washes over all creatures in the area in a glorious display of divine power. This deals damage to evil creatures and heals good creatures in the area. The amount of damage dealt and the number of hit points restored in each case is 1d8 points per 2 caster levels (maximum 5d8).
My question: Does the bloodline ability increase the health restored? My guess is by RAW, 'No, as restoring hit points is not the exact same as dealing damage even though they use similar behavior modifying the same game mechanic.'
RAI suggests to me this should count for the healing aspect of the spell too, but I don't imagine RAI gets very far at a PFS table?
The RAI seems pretty clear - if the spell is fire based, and does damage, it does extra damage. The bloodline itself offers fire-based healing abilities, so if the writer of the ability had intended for the ability to improve fire-based healing, it would probably have said so. Instead, it uses the word 'damage' twice to specify that the ability only applies when damage is being dealt.