I want to know how fiverr reporting systm works and how can we prove that we have the rights or we own this work?
Always take screenshot as a prove…
As well as screenshots (maybe including of licenses for things) you could attach things like source files to show you did the work. If Fiverr allows that in the report option. If not you could create a support ticket with them.
Keep work screenshots whenever you work. It will be convenient for you to give proof .