what is this 13 natural AC cumulative with? I know it doesn't work with armor, but what about with a naked barbarian or with a monk?
What about with a shield? Or with a cloak of protection?
The draconic sorcerer AC feature is an AC calculation, meaning it tells you how to add up your AC, and as such is not compatible with any other AC calculation.
That means not being combined with barbarian or monk unarmored defense because they, just like armor, are AC calculations.
It does, however, work just fine with anything that is an AC bonus that doesn't specifically say otherwise (and I don't recall any such things saying otherwise in regard to this sorcerer feature). So the +2 AC from a shield, or the +1 AC from a cloak or ring of protection (or both, or even a cloak and two rings) add together just fine.
The way to tell if something can be combined or not is simple: If it is worded as "+X bonus to AC" it adds with anything that doesn't specifically get called out as not adding together (like how bracers of defense specify they don't work when wearing armor).
If it is worded as "Your AC is X + Y," then it cannot be combined with anything else phrased the same way; you choose which of those you are eligible for that is most benefical.
What about a spell, such as Mage Armor?
Yes, I am confused. 
The Spell Mage Armor, states that it only works if you are wearing no Armor. I vaguely recall a comment that the features of Unarmored Defence and relatives (Barbarian, Monk, Draconic Sorcerer) do not stack with each other in the most amenable way possible. They said use the one which gives the best AC and ignore the others.
Thus if you had Characters who was a Barbarian 1, Monk 1, Draconic Sorcerer 1 lets use the following stats calculated from the standard array of 15,14,13,12,10,8. I am using Con as average and Int as the dump stat.
Gront Smashskull
Half Orc
Str:12-14
Dex:15
Con:10-11
Int: 8
Wis:13
Cha:14
Barbarian Unarmored Defense: 12
Monk Unarmored Defense: 13
Draconic Resilience: 15
Mage Armor:15
Growler Toesnapper (Anklebiter Clan)
Halfling (Lightfoot)
Str:13
Dex:15
Con:10
Int:8
Wis:14
Cha:12-13
Barbarian Unarmored Defense: 12
Monk Unarmored Defense: 14
Draconic Resilience: 15
Mage Armor: 15
Basically Draconic Resilience is Mage Armor, but bound to the skinscales, so Wild Magic Sorcerers usually appreciate Mage Armor.
Draconic Resilience will work in an anti magic zone, unlike Mage Armor.
AC i n5e is pretty simple to understand if you try to understand it.
there is 2 form of AC: formula and bonus.
A Formula AC include Barbarian/Monk/Dragon Sorcerer unarmored AC, mage armor, regular armor etc..
A Formula AC is presente under this shape: AC = X+Y... (exepction for heavy armor which are ONLY one number)
Be carefull some of those formula have prerequisite like mage armor work only if you have no armor, so if you have a leather armor and receive mage armor, mage armor duration automatically end (as describe in the spel descrition)
Some example
- Leather armor is 11+dex.
- Full plate is 18
- Mage armor is : 13+dex
- Dragon sorcerer is 13+dex
- Monk is 10+dex+wis
etc...
The formula NEVER stack together, you choose one. So you CANNOT say that you take the 13+dex from mage armor and add teh +wis from the monk. You choose between mage armor 13+dex OR the monk 10+dex+wis.
Then you got the Bonus AC
The Bonus AC include stuff like a shield, magical item like bracer of defense, fighting style and spell like Haste and Shield of faith, cover etc...
The bonus AC are presented under this shape: +X (no exception)
Be carefull some of those AC bonus have prerequisite like the defensive fighting style require you wearing an armor. Bracer of defense require you to wear no armor for example.
Bonus AC atack with EVERYTHING (except if noted otherwise in teh bonus description, like bracer of armor do not stack with a full plate AC formula, and casting 2 spell with the same name (shield of faith) do nto stack together as describe in the spell section of the PHB)
You can have as many bonus AC as you can.
So let's for fun do some example:
A Paladin/dragon sorcerer with 16dex(+3) is wearing a Fullplate (18). he cast shield of faith (+2AC) and the wizard cast Haste (+2AC) on him. He got a bracer of defense (+2 AC if not wearing armor) He uses a shield (+2AC) and is hidding behind a tree offering half cover (+2AC)
What is the AC of the barbarian:
First of all the player need to choose between if he want to wear the Full Plate (18) OR use his draconic armor(13+dex) or if he want to cast Mage armor(13+dex) since those 3 DO NOT STACK TOGETHER and THEY DO NOT MERGE. so the fullplate would offer 18 (since the dex is ignore with heavy armor) compare to 16 with dragonic armor and 16 with Mage armor. The paladin chooses take benefit of his dragonic armor since this way he can also benefit from the bracer of armor and do not receive stealth penalty.
Then we can add on that 16 all other bonuses so 16+2(shield)+2(shield of faith)+2(Haste)+2(Bracer of defense)+2(cover) for a total of 26 AC
If he would equip the Fullplate instead he wouldn't receive the bracer of defense bonus so he would have the same 26AC but with penalties to stealth