INDUCING flutter on a trainer
However, the high gain gyro instability is not likely flutter. What'd you'd probably be seeing is the feedback controller in the gyro becoming unstable.
The gyro holds a position by comparing where it wants to go (straight ahead) with where its sensor tells it it is actually going. The gyro's controller tries to drive that error to zero. The controller will multiply the error by a gain and use that to generate the servo command. If the gain is too high, the whole system will oscillate, or go completely unstable.