Now I am no historian, and I didn't make this up on my own. The interpretation offered by Jill Heydt-Stevenson is a bit convoluted but here are some excerpts:
"a flame I still deplore" refers to venereal disease.
The chimney sweep refers in part to a cure that involved applying mercury in such a way that shrouded the body and turned it into something that resembled a chimney. So the sweep (mercury) "fought the midway air,/ And soon he'd clear'd,/ with dextrous care,/ the bitter relicks of my flame."
The third stanza may refer to the folk belief that sex with a virgin offers a cure.
I also understand that to "get one's chimney swept out" is 18th century slang for sexual intercourse. (Farmer and Henley, Slang and Its Analogues Past and Present". Be on the lookout for any future JA references to chimney sweeping later in Emma.