RAW, yes Barkskin *should* set your minimum AC to 16. It should NOT stack with anything else; if you have an Unarmored Defense of 18, then with Barkskin your AC will still be 18.
Why should it not stack? Is there clarification somewhere on that? I was reading the spell, and it said:
"You touch a willing creature. Until the spell ends, the target's skin has a rough, bark-like Appearance, and the target's AC can't be less than 16, regardless of what kind of armor it is wearing."Note, it says that the target's AC can't be less than 16. It doesn't say anything about being higher than 16. Is there some kind of sage clarification for this?
That said, Barkskin is underpowered imo mainly because it requires concentration. It has such a low effect (increasing your AC by 2, maybe), such a high opportunity cost (can't cast other concentration spells), and can so easily be lost if you take damage.
Seems very similar to Shield of Faith. A plus two bonus to AC that requires concentration.