Hello senginc,
If your 31 still has the original oil seals and gaskets installed, I don't think that the flushing job as you describe will give the results that you want. There are a few things to be considered. How low are the oil levels? Where did the oil go? If the seal between the trans and rear end, located in the drive shaft torque tube, is leaking, oil from the trans migrates into the rear end, overfilling it. This puts more demand on the axle seals to prevent the oil from leaking out on the brake linings thus ruining them. Stock 31 rear ends did not come with a breather, so with heat buildup so does pressure buildup on the seals. Smooth shifting of the gears requires the heavy oil. If your gaskets show signs of seepage, they too may drip after flushing. I don't think that it would hurt any of the gears and bearings to flush them clean, but instead of driving slowly somewhere, put the 31 up on jack stands. Run it fast for a thorough flushing. Also remember to drain and service the universal ball oil reservoir at the back of the transmission. This is where the service manuals earn their keep and may provide suggestions for flushing/cleaning.
