* Part of a proper noun:
* "The Kingdom of Denmark"
* "The United Kingdom"
* "The Animal Kingdom" (this is a specific, well-known group, akin to a proper noun)
* A title:
* "The Kingdom of God"
You don't capitalize "kingdom" when it's just a general word:
* "The animals live in the kingdom of nature."
* "The king ruled over a vast kingdom."
Let me know if you have any more questions about capitalization!