How should fully cooked refrigerator stored chicken be reheated to retain moisture?
Fist, what do you mean by &quot;proper?&quot;  If your chicken was correctly cooked, then chilled to refrigeration temperatures within the window for food safety, and stored within the window of safety, you can obviously eat it directly from the refrigerator...or warm it and eat it.  No significant bacteria are going to grow, for example, if you remove it from the fridge, stick it in the microwave (or in pan on a stove) and warm it for a few minutes, and eat it. There is just not enough time for anything to incubate.  Again, the preceding assumes that you've followed general food safety protocols for your raw product, preparation, cooking, and storage...and you are consuming within the storage life of your food.
Now, if you've got some time, and your goal is to reheat to have an experience as close to the original cooking as possible, the then best tool is to use a sous vide device.  It is the most gentle and thorough tool for this job.  This is a good explanation.  All you have to do is set the device to a degree or two under the original doneness temperature, bag it, and put it in the bath.  It's the path toward moist leftover chicken...among other things.