Consider the common phrase please kindly listen while i explain this; Or kindly wait while i check this. in my view please is asking while kindly, as already mentioned, is used to take the edge. Can the word kindly be used to close an email, for example: Hi matt, i would like to thank you for the great help yesterday! Kindly, john i see it very strange, but many people in my institution.
As you have better contacts with musicians, kindly do the needful. Do the needful is used when we want to cut the story short. In fact, at times, we just write do the needful and the favorer.