These two phrases, "flesh out" and "flush out", do not mean the same thing and are not interchangeable.
You flesh out a plan. Building the plan is akin to putting flesh on a skeletal frame. Fleshing out is building up not searching out.
Your hunting dog flushes out the pheasants from the tall grass so that you can get a good shot at them. You flush out things that are hidden.
You could flesh out a plan to flush out the pheasants.
(flayed skeleton from this anatomy chart)
tags: flush out, flesh out, vocabulary