To “flesh out” an idea is to give it substance, as a sculptor adds clay flesh to a skeletal armature. To “flush out” a criminal is to drive him or her out into the open. The latter term is derived from bird-hunting, in which one flushes out a covey of quail. If you are trying to develop something further, use “flesh”; but if you are trying to reveal something hitherto concealed, use “flush.”
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