1899, Grant Allen, Miss Cayley's Adventures, ch. 3:
"You're jest about the very woman I'm looking for, miss. Lithe—that's what I call you. I kin put you in the way of making your pile, I kin. This is a bonâ-fide offer. No flies on my business!"
"He knows what we want, you bet" he whispered. "No flies on that preacher. I like him. I like any man who can do things without a diagram and directions for using."
"WestJet is tightly run, well managed, there are no flies on those guys," said Harry Gow, a board member of the Canadian Association of Airline Passengers.
Usage notes
Now usually used to suggest that a person is particularly alert, clever, or energetic.
Often used in the construction "There are no flies on him/her/them".