When I see this, I immediately think of ESL from certain parts of Asia. I’ve always suspected this has more to do with culture than language.
In the past, this type of wording was very common in translated technical manuals. For example in step-by-step instructions.
To me, substituting ‘please’ with ‘kindly’ as many Indian speakers of English do is a strange habit because this means that on top of asking someone a favor you also asking the other person to do something kindly for you. Here is the pattern:
Please answer my question.
Please answer my question quickly.
Quickly answer my question.
Kindly answer my question.
So, please don’t say ‘kindly’ when what you really want to say is ‘please’.
So, if I want visitors to remove their shoes before entering my house, it would be more polite to have a message “Please take off your shoes” rather than “Kindly remove your shoes”. Am I right?
Yes, because ‘kindly’ is not a synonym for ‘please’. At least not in modern English.
For me as a foreign learner, the word" kindly" sounds different in both sentences. In the first sentence, it makes sense because it means that “Do not close the door violently so as not to make a loud sound”, so the word “kindly” related to the act of closing the door and it has the same meaning of “gently”. In the second sentence, I agree with, Sir Torsten and, Sir Anglophile. The word “kindly” sounds odd.
Here is another opinoin “https://www.myenglishteacher.eu/blog/can-you-use-please-and-kindly-together/”
Thanks
No, there is a substantial difference in meaning between the following two sentences:
Sentence number 2 might be grammatically correct but the sentence doesn’t make sense and is not idiomatic at all.
Thank you,Sir Torsten. Ok. I think that, the sentence “please, kindly close the door” is more acceptable than the sentence “Please, close the door kindly”. Is it right or not?
Well, I recommend you stop using the word ‘kindly’ because it sounds strange and archaic. Just use ‘please’ instead.
“Please kindly respond to my email.”
The result of saying this is that you will probably get no response to your email. 
The issue here is semantic (to do with the meanings of words). If someone closes the door in a loud manner (slams to door) it can be rude, impolite, insensitive. I don’t think it is an unkind thing to do though.
I think the confusion stems from the fact that a couple of centuries ago the adverb ‘kindly’ might have been used as a synonym for ‘please’. However, language use has changed since then and if you continue using ‘kindly’ you come across as strange and archaic.
I think you could also say: Please leave your footwear outside.
It just occurred to me that some learners might be confusing ‘kindly’ with the phrase “Please be so kind as to…”
“Please kindly” is redundant, even though “kindly” is not a substitute for “please.” But, worse than that, putting the two together is obsequious – you’re stooping too low. "If my kind masters would be so inclined, I would be most grateful if you would queue up.?
I feel the more gentile way of saying “please leave your shoes at the door” would be “kindly leave your shoes at the door”. I use this when speaking to a above general use speaker. It’s not archaic and I feel some of the responses you have got are not understanding your question.
It’s one question what you ‘feel’. It’s a completely different question how native speakers use the language. We have tried to explain to you that using ‘kindly’ instead of ‘please’ is outdated and sounds archaic. Why are you bringing it up again?
Your opinion. But not the norm of you have a British background.
It turns out we have had the same conversation quite a while ago:
Thanks for your question. Had doubts are this words synonyms or not
My two cents: I would agree to not use them together, but I use both fairly often. As an attorney (in the US), in a cover letter I may write something like, “Enclosed please find…” and then later may say, “Kindly sign and return…” so the use of one versus the other could simply be to avoid repetition. But not to put too fine a point on it, I will say that “Kindly” seems to make more sense with an imperative: “Kindly close the door” versus “Close the door.” sounds softer. And i would not likely use kindly as much in spoken speech - and when I do, it’s usually, “Thank you kindly.”