Capitalize "Kingdom" when:
* It's part of a proper noun:
* Kingdom of Saudi Arabia: Here, "Kingdom" is part of the official name of the country.
* The United Kingdom: Same applies to this country's official name.
* The Animal Kingdom: This refers to a specific, well-defined taxonomic group.
* It's used as a title:
* The Kingdom of Heaven: This is a religious title.
* King Arthur and the Knights of the Round Table: This is a specific work of literature.
Don't capitalize "kingdom" when:
* It's used as a generic term:
* "The lion is the king of the animal kingdom."
* "The plant kingdom is vast and diverse."
* It's not part of a proper noun:
* "The king ruled over his vast kingdom."
In doubt?
If you're unsure, it's always best to check a style guide or dictionary.