"Kind", "Kindly", and the Google Method

I was recently confused by the subtle difference between these two words, "kind" and "kindly."

Specifically, when following up E-mails, I was not sure to use "thank you for your kindly reply" or "thank you for your kind reply".

One of my friend suggested me to use an interesting method: just Google the two sentences, entire two sentences, and see which one occurs more frequently than the other. The "kind" turned out to be the majority; but some people do use "kindly" in their E-mails. Still, I am not sure about the difference. Finally, www.m-w.com, the Merriam-Webster online, came to my mind. I then decided to throughly dig out the exact meanings of these two words from m-w.

After a few minutes interpreting (overly?) concise outputs from m-w, I got the answer: the more appropriate word is "kind", which is the same outcome suggested by the Google method. Cool!