There's some unique flute playing on the song. It has a story behind it that Cave shared in Red Hand Files #113
(the Red Hand Files
are Cave's email newsletters to fans).
Bad Seed Conway Savage had threatened to shove Bad Seed Warren Ellis' flute up Ellis' "arse" if he ever heard him play it again. Ellis took the threat seriously and didn't touch the flute for over 10 years. Cave asked Ellis to play it for "Breathless." Ellis did, but what came out was terrible (by Cave and Ellis' estimations), no doubt largely because he'd not played the flute in a decade.
They gathered all the flute takes and did everything they could to make it work. As Cave explains: "So, Nick Launay, the producer, messes around with the flute, and then plays all the takes back at the same time - some backwards, some detuned, some phased - and it sounds like an incredibly f--ked-up 14th- or 16th-Century style ensemble."