Well, this is an easy one to fix. You definitely only need to capitalise the first letter, like this: 'Kind regards'. Speaking of which, if you're confused about which sign-offs are okay, and which are a professional no-no, read our article on the best ways to start and finish an email.

Do you capitalize both words in a closing?

The rule is to capitalize only the first word of the close. This rule applies wherever you use a complimentary close: emails, letters, notes, and even texts.

Should regards have a capital R?

When you are using “Best regards” as a closing to an email or letter, it is advisable that only the first word should be capitalized. That is true for “Best regards” and every other phrase that comes at the end of a letter or email, such as Sincerely yours, etc.