While there is no standard format for closing emails, I think there are very few situations in which best regards and kind regards would be considered too informal.
They are what I would call semi-formal expressions and you can use them to sign off most formal or business emails.
Formulas such as Love, Yours, or Thanks, are the ones that are generally considered too informal, and are used only when writing to friends or relatives.
To learn more about formal and informal correspondence, read Formal and Informal Email Phrases – from Greetings to Closing Phrases!
