Identifying flowers is easy compared to identifying figs. There are hundreds of varieties grown around the world. Some are only capable of being grown in a certain part of the world.
Ray Givan is a Georgia fig expert who has an extensive collection of figs.
He has kindly put together a guide to fig identification based on the fruit skin color.
Also see this fig monograph written by Ira Condit in 1955.
This LSU fig publication is very helpful.