The term "Flying Top" is perhaps unique to the Mills canvas jargon, and would otherwise be called a small Bimini Top.
The Flying Top was part of the Mills Weather Canvas set and integrated with with the Windshield, the Side Curtains, the Drop Curtain, and for an open boat, the Forward Shelter.
Mills also made a much larger top, which they called a Sun Top. The Sun Top would not be able to integrate with the rest of the Weather Canvas system.
A Wm. J. Mills & Co. FLYING TOP as seen on a REVENGE 22 W-T Whaler Drive boat.
In this view the Drop Curtain and the Port Side Curtain are removed. The Windshield and the Starboard Side Curtain are in place.