According to the Oxford English Dictionary (https://en.oxforddictionaries.com/definition/fly): ----------------- (there are) no flies on — Used to emphasize a person's cleverness and astuteness. ‘no flies on Phyllis—she paid six months in advance’ ----------------- This is the way that I've always heard it used. The intended meaning is that the person is too clever to allow flies (that is, insects) to land on them. In some cases it also means that the person is moving too fast for the flies to land on them; they are a few steps ahead of other people. As to your question of whether it is common; in Australia it was probably more common 40 or 50 years ago, and you're more likely to hear older people say it. It's less common with younger people. (Or that has been my experience, at least.)

Flies or flaws?

It is an outdated expression in US English. I've read it in dialog in old books. I've never heard it used in real life in my lifetime. It's usually used in the first person, "there ain't no flies on me." It means "I am active, I am alert, I am not naïve, I am not gullible, you can't fool me." A folk song or songs has various versions of the refrain, "Oh, there ain't no flies on me, there ain't no flies on me There may be flies on some of you guys But, there ain't no flies on me!"