I don't see why those two are incompatible. The multiclassing rules say that you can't gain the Unarmored Defence feature from two classes. It doesn't mention Draconic Resilience. Am i missing something?
It's been ninja'd, but you need to look at how they are worded. They are completely separate equations in overall "determine AC" equation. It's a basic IF-THAN statement that doesn't overlap. Unlike previous editions, where many of these rules were phrased as "Add X modifier to AC if this prerequisite is made", 5e says, "if this prerequisite is made, then your AC is this."
Forgive the analogy, but think of it like this.
If you have the sun skill, if it is sunny, your AC is 16+int
If you have the cloud skill, if there are clouds, then your AC is 17+dex
If the situation arises where it's sunny and there are clouds, you don't add them together. Let's say you have an INT modifier of +2 and a DEX modifier of +2. So your AC is either 18
or 19. If you were to write this as an equation, the first step gives you an 18 AC. But then it checks the next rule, which changes your AC to 19.
I.e.:
If "sunny" than AC=(16+INT Mod)
If "cloudy" then AC=(17+DEX Mod)
Only one of those can be a valid value at any given time.