I would assume that given writing for the pulps meant writing quickly in order to earn sufficient for rent and groceries that the borrowing of colour and settings was common practice. It wouldn't need to be entirely within genre either so while Burroughs' Mars was probably Leigh Brackett's source deserts were a pretty common setting for all sorts of adventure stories.
In regards to skirling flutes however while I will grant you that this was probably in imitation of Lovecraft I doubt he had the Arabs in mind. Lovecraft's inspiration for blasphemous flutes was much more like to be the Pan pipes, the multi-barreled flute played by the Greek god Pan. Pan and his pipes was a common symbol for paganism and in one form or another turned up frequently in fiction. In particular Lord Dunsany (whose fiction Lovecraft was especially fond of as you know) featured the flute music of Pan in his novel THE BLESSING OF PAN as a sort of mind altering substance. Given this obvious tradition Occam's Razor states that this is where those blasphemous flutes most likely came from.
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In regards to skirling flutes however while I will grant you that this was probably in imitation of Lovecraft I doubt he had the Arabs in mind. Lovecraft's inspiration for blasphemous flutes was much more like to be the Pan pipes, the multi-barreled flute played by the Greek god Pan. Pan and his pipes was a common symbol for paganism and in one form or another turned up frequently in fiction. In particular Lord Dunsany (whose fiction Lovecraft was especially fond of as you know) featured the flute music of Pan in his novel THE BLESSING OF PAN as a sort of mind altering substance. Given this obvious tradition Occam's Razor states that this is where those blasphemous flutes most likely came from.