said to be a humorous title for a chimney-sweep, 1947 according to OED, from flue + ending from economist, etc.
Entries linking to fluonomist
flue n.
"smoke channel in a chimney," 1580s, of uncertain origin, perhaps related to Middle English flue, flewe "mouthpiece of a hunting horn" (early 15c.), which is perhaps from Old French fluie "stream;" or the modern word is perhaps from Middle Dutch vluwe, from Germanic *flowan "to flow" (see flow (v.)). Originally a small chimney in a furnace connected to the main chimney.
economist n.
1580s, "household manager," from French économiste; see economy + -ist. Meaning "student of political economy" is from 1804.