Sorry J, this one's going to require refinishing.
The problem is that you would never be able to level out the new finish with the old layers and it likely wouldn't stick well to the old finish anyway. When small chips happen, I stabilize them with a little clear fingernail polish but you've got some major slabs of finish flaking off so it goes way beyond a "quick fix".
Fortunately, a clear coat alone won't cost the same as a complete repaint with a clear coat.