I’ve given police dirty looks and honked at them a few times, for things like setting up a speed trap in dangerous (to non-speeders) or safety-irrelevant places, but that was impulsive and probably unwise.
At most I would report whatever I was concerned about to the police office, not the officer.
I would not chase after speeding officers. Officers are trained to drive fast safely, and are allowed to exceed the posted speed limits if they have a reason. People aren’t supposed to interfere with their work without a good reason, and if they’re speeding they may be responding to an important and possibly dangerous situation, so rushing off there too and questioning them about their speed seems like a bad idea on many levels.
I once told an officer who seemed to be relaxed but was headed towards some fast food, about a dog that had been hit by a car. He looked really angry with me and zoomed away without saying anything. So I can imagine it might be dangerous to chase down a speeding officer to give them a hard time about driving fast.