Depends on your definition of a "Flying bicycle". There's been a couple of successful, pedal-driven airplanes. Gossamer Albatross probably being the most well known.
Then there is any number of people who've strapped a bicycle to themselves prior to some paragliding or hang gliding. Tend not to work very well, people don't have enough hands to control both bike and wing simultaneously. Something that's inherently stable, like a trike, would work better. But then, by definition, it's not a bike anymore.
As for a pedal-driven helicopter, forget about it. Humans simply don't have the power-to-weight ratio to pull that off.