See the song in the DT called THERE AIN'T NO BUGS ON ME. It has an alternate chorus that begins "There ain't no flies on me."

SILVER JACK also contains the line, "Stack your duds and cut your capers, for there ain't no flies on me."

There is a discussion in the thread Question: Duds & Capers, what are they.

I take it to mean, "I don't stand still enough to attract flies. I'm not lazy or idle like some of you guys."