adverb
1
BAD : You are very kindly to spare me so much of your time.
GOOD : You are very kind to spare me so much of your time.
BAD : She is always very kindly and helpful.
GOOD : She is always very kind and helpful.
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Kindly is nearly always used as an adverb: 'They've kindly offered to lend me their car while they're away.' 'Would you kindly sit down and stop being a nuisance.'
2
DUBIOUS : I wonder if you would kindly correct my mistakes.
GOOD : I wonder if you could possibly correct my mistakes.
DUBIOUS : Would you kindly open the door?
GOOD : Would you mind opening the door, please?
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Kindly is used to mean 'please' only in formal styles. When used inappropriately, it can sound sarcastic or even express anger: 'Would you kindly keep your hands to yourself.'