When we want to be polite in English we usually try to be understated and vague. In general the more remote and vague the language used, the more polite and we are being, and also the less likely it is that we will cause offence. Remote language will, for example, use hedging as well as modal devices such as if that's at all possible, by any chance, if you wouldn't mind, as well as the actual use of the remote modal verbs would, could and might.
One of the problems with kindly is that, far from being vague, not only is the speaker asking us to do something, but they are very specifically telling us how to do it. The use of the word kindly presupposes that we need to be told this, in other words it implies that if they didn't say it they feel that we would be inconsiderate or uncooperative.
One last issue here is the placement of the word kindly, which has some similarities with the item please. The least direct place to put please is at the end of the sentence, where it would fall outside of the head of the intonational phrase, instead appearing in the tail, where it is out of focus. Nice and subdued then.
Slightly more entreating and direct, but still fine, is at the beginning of the sentence, where it will be the first stress in the sentence and thereby form part of the head of the intonational phrase.
However, when we put it in the post-auxiliary position it makes the utterance less of a request and more of an order. It has the effect of making the 'request' much more direct. I suspect the reason for this is there is a huge contrast in pitch between the pre-head (the first few unstressed words in the utterance) and please, making the latter very prominent. Please here will still be the onset of the head, but more marked in this position. The preceding material is likely to be said quietly and at a lower pitch. Please on the other hand will be the first high pitch, loud syllable and will contrast markedly with what came before. (The reason for this, is that we like to put old information at the beginning of the sentence, and so, being old, this will be de-accented.)
Compare the following:
- Could you give me a hand, please?
- Please could you give me a hand?
- Could you please give me a hand!
One of the problems with kindly then, when used like this, is that it usually appears in the post-auxiliary position and cannot appear at the end. This gives it a too prominent position in the sentence, doubling its perceived crimes.