Does Ki Barrier stack with each other?

Yes — two Ki Barriers stack, giving the unit a combined 14 damage prevented this turn.

Each Ki Barrier creates its own separate Prevent pool (Prevent 7) tracked on the unit (Rule 437.1.b.1). When damage would be dealt, both replacement effects apply in the order you choose (Rule 372), so the first pool absorbs up to 7 damage and the second absorbs whatever remains, up to another 7. Rule 437.5.a also confirms the game considers "the Prevent Value of all Prevent Actions on a Unit" together when calculating lethal damage. Unused prevent value from the second copy carries over normally if the first is fully spent.