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Damage Reduction and Fire Resistance are different things.
Flame Touched gives you DR 1/- against fire creatures... but DR does not apply to energy attacks. So, if a red dragon bit you the DR 1/- would apply, if it breathed fire on you the DR 1/- would NOT apply.
Fire Supremacy grants fire resistance 5... which works the opposite way, it would reduce damage from a fire breath weapon, but not damage from a bite attack.
DR reduces physical damage. Resistance reduces energy damage.

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Does the flame-touched trait that grants DR 1 against fire creatures and attacks stack with the wizard elemental fire school ability Fire Supremacy that grants resistance 5 to fire for a total of resistance 6 to fire?
CBDunkerson has it right. The DR would apply to physical damage dealt and the fire resistance would apply to fire damage.
So they could sort of stack, with regard to a single attack that deals both fire damage and physical damage. They don't stack, but they could both apply to a single attack.
In example, if a creature with the fire subtype attacks while wielding a torch as an improvised weapon, the DR would apply to the bludegoning damage of the attack and the fire resistance would apply to the fire damage part of the attack.