This will be clarified in the next rules update. The clarification that will be made is as follows:
- The term "damage barrier" in these rules refers to the effect itself, not to the card providing the effect. (This is necessary, because future effects may give Damage Barriers without the Damage Barrier being tied to a particular card.) Thus the Circle of Fire, for instance is not a damage barrier itself; it is an enchantment that provides a damage barrier.
- As always, if multiple continuous effects affect the same object, they are applied in timestamp order. (Thus, since you can only have one Damage Barrier, the first effect providing a Damage Barrier will function, then the next effect providing a Damage Barrier will fail to function.)
In other words,
- If you put on the Demonhide Armor and then reveal the Circle of Fire, you will have the armor bonus from the Demonhide Armor and the damage barrier from the Demonhide Armor. (If the Demonhide Armor is later destroyed, its damage-barrier-providing effect will go away, so you will then be able to use the Circle of Fire's damage barrier.)
- If you reveal the Circle of Fire and then put on the Demonhide Armor, you will have the armor bonus from the Demonhide Armor and the damage barrier from the Circle of Fire. (Again, if the Circle of Fire goes away, the Demonhide Armor's damage barrier will begin to function.)