It’s not as complicated as that post makes it seem. Calculate your AC as if you didn’t have Barkskin. If that number is less than 16, Barkskin brings your AC to 16 (because the effect of Barkskin is that your AC can’t be less than 16.) If that number is 16 or greater, Barkskin has no effect (because your AC is not less than 16.)
Except that that is not what the spell says, at least to me. Consider the two following wordings:
Not the PH said:
the target's AC can't be less than 16, regardless of what its AC would be otherwise
PH said:
the target's AC can't be less than 16, regardless of what kind of armor it is wearing
If the spell read as in the first wording, I would agree with you. However, what we actually have is the second. So I would modify what you said to be the following:
Calculate your AC based only on what armor you are wearing, that is, according to the table on page 145 of the PH (or 10 + DEX mod if you are wearing no armor). If that number is less than 16, Barkskin brings your armor-based AC to 16 (because the effect of Barkskin is that your armor-based AC can’t be less than 16.) If that number is 16 or greater, Barkskin has no effect (because your armor-based AC is not less than 16.) Then modify your AC according to items/features that usually modify your armor-based AC, such as a shield.
To me, the only thing that could be controversial is the treatment of your DEX modifier. One could argue that if a character has only Barkskin and no armor, then its AC should be 16 + DEX mod. I think that is not RAI because
a) It is a general rule that how DEX affects AC depends on armor type. Since the Barkskin effect is, effectively, armor, and its description says nothing about adding your DEX mod, that means you don't add your DEX mod. It is analogous to the lines for the heavy armor types in the table on page 145 of the PH. (In fact, since the AC that it is granting is 16, it seems very reasonable to treat it similarly to a heavy armor, except for the fact that you can, if you choose wear a more protective armor over it, provided you can find some that a druid can wear.)
b) If you did add DEX mod, a druid with Barkskin, a shield, and a DEX of 14 would have an AC of 20. To me, that seems quite unlikely to be intended (but this is, clearly, subjective).
Finally, I guess, a word about shields. I am not aware of any instances in the 5e rules in which the word "armor" is intended to include the use of a shield. And in the specifications of Unarmored Defense feature for Barbarians and Monks, whether a shield is allowed is made explicit. So my take is that "what kind of armor it is wearing" does not comprehend shield use.
All of which amounts to what
@DEFCON 1 said rather more concisely, um, 5 1/2 years ago.
The way I read it... you have a floor of 16 for AC due to armor, and it can go up from there with anything else besides armor that normally raises your AC.
Oh, and then one last word about why the way the spell is written is absolutely terrible and subject to so much discussion. The fundamental flaw is simple (and, I would think, obvious to a competent author): basically, instead of telling you what the target's AC
is, it tells you what the target's AC
isn't (it is not less than 16). Would it have taken a few more words to say, explicitly, how to calculate the target's AC? Yes. Would it have eliminated a lot of DMs spending time - time that could have been usefully spent otherwise - trying to figure out WTF they meant (or, failing that, how I want it to work) because even though I don't care a lot about how exactly the spell works, I have to make a decision? Also, yes.