I had this same issue on one of my Ballys.  With the flipper button depressed, a bit of finger pressure on the tip of the flipper would cause the "chatter".  I dug a bit into the web, and the solution (at least in my case) was replacing the coil stop.

If you simply change the coil stop with a coil stop in the game from another coil (try the other flipper's coil stop), see if that fixes it.  Coil stops become magnetised (and mutilated) over the long haul from the constant hammering.