While this may well level a warped piece of wood it won't aid in the two sides flexing equally. If the mismatch is extreme you may well need to cut one or even two sides from new wood.

An old trick from the books I read on model building showed how to compare sheets for similar stiffness for matching things like sides. It involved holding the sheets so that they hung over the edge of the bench like two diving boards with only about 2 inches held onto the bench. For wood up to 3/16 inch you look for the wood to sag by equal amounts to show that they were about the same bending stiffness. This is more effective with wood of 1/8 inch or less. With 3/16 stock I suspect it would work as well but you would want to position a little extra weight at the end. Something like an oz perhaps? That would cause them to sag enough that it would be far easier to see what their relative stiffness' are like.