Having this issue as well. Purchased the Lego set, applied the code yesterday. 24hr later, the skin pack is still not displaying in Minecraft (bedrock) v1.13.1. This applies to both the Switch and Windows 10 edition.
I have a similar issue with a Kindle Fire. Minecraft loads fine but as soon as you click on "Play", it crashes. The only workaround I've figured out is to:
1. Open Minecraft
2. Click on "Sign In"
3. This opens an Xbox modal to sign in with Xbox, continue
4. As soon as the Xbox Live sign up screen displays, hit the back button
5. This will take you back to the Minecraft start screen
6. Click on "Play" and it works
Still not showing up and now using version 1.14