DO you have an auto trans? I could believe a flexplate to be broken but not a flywheel, if your flywheel is broken you`d either be picking up the pieces scattered all over the road. or at least have a terrible vibration!
If so, there should be small inspection cover behind oil pan or on bell housing, it may be hard to see but typically cracks develop between the bolt holes on the flexplate, and can cause clicking clanging noises, typically right after startup, and can sometimes go away when warm, or appear at certain rpms.