For example, how many hp are healed by a barbarian 8/life oracle 1 that possesses the feat Fire God's Blessing when he deals damage to a foe with his +1 flaming greatsword?
Yes, it does.
The effect of the feat says:
Whenever she is subject to a spell that cures hit point damage, she heals 1 additional point of damage per caster level. In the case of non-spell healing effects (such as channeled energy or lay on hands), she heals a number of additional points equal to the class level of the character performing the magical healing. This does not affect fast healing or regeneration.
Both Lay on Hands and Channel Energy are supernatural effects that can heal damage. There is nothing on their description that makes them anything special regarding how to classify their effect, neither are classified as fast healing or regeneration either.
- spell level + character's class level hit points.
For Fire God's Blessing, the use of the ability seems unintended and stronger than it should be, luckily, it is limited to once per round. But this looks valid from the rules as written, and the character would heal for:
- character's class level + 1 hit points.
However, if both effects are used, i wouldn't let you to get healed twice your level. Because the source of the extra healing is the same (the rage power), and the character would heal for: character's class level + spell level + 1 hit points.
If the class that granted you the rage power is the barbarian, you should replace character's class level by your barbarian levels.
Keep in mind that to qualify for Fire God's Blessing, the character must worship the Fire God (this info was removed from SRD), a deity specific to golarion that is worshipped by certain orc tribes (more info on Orcs of Golarion). The Belkzen, Hold of Orc Hordes campaign setting book revealed that this deity is known as Sezelrian. Of course, nothing stops your GM from converting this to any other setting.