Not only is it, as ASFKAP mentioned, legally a "No Go" item if it isn't in the MEL, but from an engineering and safety perspective it should be a "No Go" also: you have something wrong with your stab system (whether the motor or the control unit) and that's hardly a trivial system.
The higher trim motor rate when flaps are down/in motion is presumably because it's required, so you may not have the requisite amount of handling. If your aircraft has a flap/stab interconnect, chances are the trim command in response to flap motion is for a number of seconds, not for an actual stab change, so if the rate is wrong, you'll get the wrong amount of stab as a result.
You also don't know if anything else is kaput in the stab system. Inflight would be a bad time to find out.