"Kindly" is often used in a polite request of someone else, and the word usually follows the word "you." For example: "Would you kindly stop smoking?" "Would you kindly put that away/" "Would you kindly shut up!" It is more common to say: "Would you please stop smoking?" Native speakers will sometimes use the word "kindly" instead of "please" to indicate mild frustration or anger. For example: "Would you kindly stop talking on your cell phone here in the restaurant? You are bothering me."

I wouldn't put kindly and please together. Kindly is a substitute for please. You can use them in different parts of the sentence, though: Would you kindly stop smoking, please? Note that neither kindly nor please takes a 'to' in front of it.