Yes.

The actual rules for this are oddly worded, but the notation is pretty simple.

In general, there are two formats for "things that increase your AC." The most common format is the one attached to armor:

[your AC equals] 11 + Dex modifier

or Draconic Resilience:

your AC equals 13 + your Dexterity modifier.

Note that there is no "plus" at the beginning of the formula. These items set your AC to a specific value.

The other format is that used by shields and class features that increase your AC above its base value:

Defensive fighting style:

You gain a +1 bonus to AC.

Or a shield:

Wielding a shield increases your AC by 2.

These are phrased in terms of increasing, rather than setting your AC. They are preceded by the phrase "increases" or a plus sign.

So, it's pretty simple. You get one thing that sets your AC, and any number of things that modify it (except where restricted by other rules, like the rules stating you can only use one shield).

A fighter could very easily have an AC like this:

[15 + Dex Mod] (half-plate) [+2] (shield) [+1] (defensive fighting style)

For a total AC of 18 + Dex Mod.

But he couldn't add a chain shirt to increase his AC, because both that and the half-plate set his AC to a fixed value.

The same applies to Draconic Resilience. You can stack it with a shield, because a shield increases AC. And you can further stack on the Shield spell, giving you a (temporary) total of [13 + Dex Mod] [+2] [+5], or 20 + Dex Mod.

But you can't combine Draconic Resilience with Mage Armor, because both Mage Armor and Draconic Resilience are trying to set your AC to a fixed value.

Some things Draconic Resilience stacks with:

• Shields

• Shield spell

Some things it does not:

• Plate

• Mage Armor spell

• Barbarian Unarmored Defense class feature

RAW

The rules for AC are on page 14 of the Player's Handbook, or page 9 of the Basic Rules.

The relevant part is this:

Without armor or a shield, your character’s AC equals 10 + his or her Dexterity modifier. If your character wears armor, carries a shield, or both, calculate your AC using the rules in chapter 5. Record your AC on your character sheet.

[...]

Some spells and class features give you a different way to calculate your AC. If you have multiple features that give you different ways to calculate your AC, you choose which one to use.

The rules called out above appear to be these:

Wielding a shield increases your Armor Class by 2. You can benefit from only one shield at a time.

If you wear light armor, you add your Dexterity modifier to the base number from your armor type to determine your Armor Class.

(and so on, for each type of armor)

The rules are sloppy here. Technically, they don't give you a calculation for AC when wielding a shield and no armor. And they never explicitly call out what is or is not a "way to calculate your AC."

With that said, we can use examples to build the intent of the designers.

It's pretty clear that you don't have to choose between a shield and plate. It's also pretty clear that a shield shouldn't set your AC to 2.

Finally, it's pretty clear that wearing a chain shirt with half plate shouldn't set your AC to 28 + 2 * Dex modifier (max 2).

It seems obvious then, that a "calculation" is something that sets your AC to a value plus other modifiers.

If something just adds on to (or increases) your AC, you continue to use whichever calculation is most favorable plus the new modifier.

This is really strong, at least for certain builds. Anyone who wanted to focus on Str anyway is likely to end up playing this race.

Firstly, Barbarians. Barbarians are currently one of the most MAD classes in 5e, needing good Str, good Con, and at least reasonable Dex. Your race would allow them to dump Dex and just focus on Str and Con.

Secondly, Druids. This is probably the worst case - your proposed race gives a Moon Druid an incredible boost to their Wild Shape forms. Str and Con are the strong points, and AC is the weak point, of most beasts, especially the ones Druids like to Wild Shape into.

Next, Fighters. This is the least problematic, since a Fighter could already afford to focus solely on Str and Con, but it does mean they end up with a better AC than they otherwise would have.

Oddly enough, it also enables Str-based Monk and Rogue builds. This isn't really a problem though, since in many ways Dex is inherently stronger than Str anyway.

Comparing it to Monk isn't really that useful, since they're essentially the same, but anyway:

• Level 1: Typical Monk has 16 Dex and 16 Wis, giving them an AC of 16. A Barbarian of your proposed race has 17 Con and 15 Str, giving them an AC of 15, or 17 with a shield.

• Level 4: Typical Monk has 18 Dex and 16 Wis, giving them an AC of 17. A Barbarian of your proposed race has 18 Con and 16 Str, giving them an AC of 17, or 19 with a shield.

• Level 8: Typical Monk has 20 Dex and 16 Wis, giving them an AC of 18. A Barbarian of your proposed race has 18 Con and 18 Str, giving them an AC of 18, or 20 with a shield.

• Level 12: Typical Monk has 20 Dex and 18 Wis, giving them an AC of 19. A Barbarian of your proposed race has 18 Con and 20 Str, giving them an AC of 19, or 21 with a shield.

• Level 16: Typical Monk has 20 Dex and 20 Wis, giving them an AC of 20. A Barbarian of your proposed race has 20 Con and 20 Str, giving them an AC of 20, or 22 with a shield.

Your proposed race can always have a better AC than a Monk of the same level if they choose, despite the inherent weakness of starting with +2 in a single stat rather than +1 in two stats.

You're right that basing it off Dex and Con would be even stronger, but only because Dex is inherently stronger than Str. Your footnote about bonuses, however, is less accurate. A minor bonus to AC, while good for everyone, is hardly a game-changer. Your proposed feature, on the other hand, can form the foundation of a build. It replaces a core feature of the Barbarian or Monk, and is effectively completely free, especially since your proposed race has fire resistance on top of it.