"would you kindly" is correct and usable in written English. It is an expression used to make a polite request. For example, you could write, "Would you kindly answer a few questions about the project you're working on?".
Would you kindly ask me about individual phrases.
> particular law, in Hebrew or English, would you kindly contact me.
So would you kindly advise if there is any New York, N.Y. in the United States.
Would you kindly send us a) a civil answer to this letter b) immediately.
M. HERZOG: Would you kindly explain to the Tribunal under what circumstances you were appointed to that office?
So would you kindly advise if there is any New York, N. Y. station in the United States.
Could I please stop receiving all messages about Farmville (I don't play Facebook games and so they're really not my thing) and would you mind kindly just sending me a puppy update once a week?
Why would you not respond kindly back?" Which I understand this thought ― really, I do.
Adrian A. Buck, a Gorham representative writes "to ask you if you would kindly permit us to exhibit in our window, the bronze bust of 'Darwin' by 'Couper,' as we should like to exhibit so worthy a piece" (AMNH archives 1909, April 7, Buck to Bumpus; April 9, 1909, Bumpus to Buck; Anonymous 1909g).
I thank you for making it possible for me to receive them, and I should be grateful if you would kindly inform the friend, should you be in possession of his or her address, that I greatly appreciate this valuable present.
My uncle entered the room, still dirty from digging the cat-hole, and said kindly, "Adira, would you like a foot rub?" and the girl tensed and a small "Nnnneh" sound came out of her mouth, and my uncle sat down next to her and began rubbing her feet.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK