More specifically the small and subtle creases/bends you see in the flag.
As of now I have a plane with a cloth tag attached and have spent hours messing with the different settings/ fixing points but I can never quite match the simple creases in the example image. I need my flag to be less bulky and much more subtle. My version:
without seeing the scene file, generally you can't get fine detail unless the cloth is subdivided enough (and the noise moving the flag would have to be pretty fine too - though that depends on how you are moving it I think)