I couldn't quite follow your logic, but this is how barkskin works.

• If your AC is less than 16, it is now 16.
• If your AC is greater than 16 it is not changed.
• If your AC was less than 16 before you cast barkskin, so it is currently 16, and then something changes to improve your AC further, then you calculate your AC with the new item ignoring barkskin. If the new AC is still less than 16, it's now 16. If the new AC is greater than 16, barkskin has no effect and you can stop concentrating on it.
• If your AC was higher or equal to 16 before casting barkskin, but then something happens which causes your AC to go below 16 while the spell is still active, your AC is 16.

What this means is that other factors are more relevant than the thickness of your skin, once you go above an AC of 16. To explain further, your skin is your "last line of defense". If you have a shield and armor, and those combined do not yet equal 16, then an attack that gets past your shield and armor gets to your skin, which because of the spell is a 16. However, your skin does not increase your effectiveness in using your shield and armor, so if your AC before the spell is greater than 16, your skin offers no extra protection beyond this. Since AC is an abstract concept which involves your many different ways of defending yourself, that which protects you best is the defining characteristic of your AC.

Being that this is a second level spell only available to Druids and Rangers and Nature Domain Clerics, the odds of having a dex of 20 to get a +5 to your dex modifier is very low, for at least another 5 levels. (This spell only becomes available at 3rd level)

The ring of mystic fire only affects the upcoming spell once

The ring of mystic fire (Magic Item Compendium 125) (7,500 gp; 0 lbs.) does, indeed, grant "a bonus to the amount of damage you deal with the next fire spell you cast before the end of your turn," but the ring only grants that bonus once. Each ray of a scorching ray spell isn't the spell; instead, the whole spell creates multiple rays. The ring improves the spell's damage only once by a maximum of +4d6 no matter how many effects result from the ring-modified spell.

(Ruling that each ray of the scorching ray spell benefits from the ring multiplies the power of the ring by the number of rays—with rather extreme consequences at low levels, especially given that the ring increases also the wearer's caster level for fire spells!)

Although the DM has several options available to adjudicate the ring's effect—allowing the player to distribute the total number of extra dice damage the ring grants among the rays before (or even after) the rays're launched, for instance—, this DM would keep things simple and have the player add the extra damage to his PC's first ray in a volley from the spell scorching ray, in much the same way that precision damage applies to the first attack in a similar volley (Rules Compendium 42). (In fact, I have a fire wizard in a current campaign who's eyeing this very item, and that's how I'm ruling it works.)

Hence, for example, under such a ruling, a level 6 caster wearing a ring of mystic fire can take a swift action to spend 3 of the ring's charges. Then the caster can cast scorching ray, creating 2 rays (because of the increase in caster level granted by the ring) and making 2 ranged touch attacks. If the first ray hits, it deals 8d6 points of fire damage. If the second ray hits, it deals 4d6 points of fire damage.