Have you ever worked with gumpaste roses and broke one petal as you were trying to arrange them in a cake? It has happened to me and this is the way I fix them so I can still use it. I don't recommend using this with competition cakes since you are supposed to be showing your best work. This is something I have used while making a wedding cake and I make sure that the broken flower is at a spot that

won't show it has a break. 
This technique works great with clean breaks. If your flower breaks into a million pieces I would say just throw it away and make a new one. I hope you enjoy this tutorial.