Can the two phrases above go together, or just one use either please or kindly.
e.g. please kindly provide me an authority letter or kindly provide me an authority letter?
Normally, you can use just one of them. You can use either 'please' or 'kindly'. It isn't necessary to use them both. However, sometimes using them both together lays more emphasis on the speaker's politeness. Although some people might see that 'kindly' is redundant here, it actually intensifies the speaker's politeness.
BTW, I think you should insert the preposition 'with' above (provide me with ...).
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