My reading of it is that Grayflame adds +1d6 of damage, similar to the "divine power" portion of the damage from Flame Strike.
A flame strike evokes a vertical column of divine fire. The spell deals 1d6 points of damage per caster level (maximum 15d6). Half the damage is fire damage, but the other half results directly from divine power and is therefore not subject to being reduced by resistance to fire-based attacks.
Emphasis mine. The point is that it's not fire damage (i.e. subject to Fire Resitance/Immunity), but Divine damage. The reference to Flame Strike isn't anything more than demonstrating the difference between Fire damage and divine damage. The target is not subject to a Reflex save for half.
There's no reflex save. If it were to have the Reflex save, it'd say something along the line as "of the flame strike spell", which it does not.
I suppose the mention of Divine Power in the damage indicates that there might be no Reflex save needed. I saw that too but wanted to see if I was interpreting that properly. It's strange that it mentioned Flame Strike at all.
It's "divine power", as per "damage source": in flame strike description, it's says that hal damage is fire and half come directly from the raw power of deities. The latter is the exact type of damage dealt by grayflame enanchment. Flame strike works differently: it allows a Ref save to halve total damage. Eg, you're 10ish, flame strike deal 10d6 damage (let's take a value of 36). You roll the save, if you fail you take 36 point of damage, 18 are fire damage, so if you have fire resistance you can reduce this damage, and 18 are raw divine power, aggainst wich no reduction works. If you succed the save, you halve the above values, without changing anything. There's no correlation by the mention of divine power in the enanchement and in the spell. The only connection is that's the same type of damage, which is divine raw power.