If you
really want the answer, ask
Michael Dresdner. And you should pay him the $20 he asks for when helping people out.
There are a number of potential problems with trying to fix the flaking paint. In no particular order:
1. Some clear coats aren't really clear; they'll add a color cast that may make the paint look different. Oil-based clear coats tend to add a yellow or amber tint. Water-based clear coats, especially the Varathane products I've used, tend to add a bluish tint.
2. The clear coat may contain the solvent for the paint! This is the absolute worst-case scenario: you don't know what is in the paint, you start spraying a clear coat over it, and the whole thing starts to drip and run! This is probably most likely to happen if you spray a lacquer-based clear, but I would suggest testing anything on a small, inconspicuous area before using it on the entire cabinet.
3. Fixing the flaking problem won't fix the rest of the paint job. For your pictures, it looks to me like there are some waves and bubbles in the paint. Spraying a clear coat over those won't fix them; they'll still look damaged. And there's a good chance that, even with a clear coat, they'll eventually flake off.
4. Make sure you use a gloss level that is appropriate for the project. I'm of the opinion that a high-gloss finish is almost never appropriate. The surface must be absolutely
perfect if you're going to use a high-gloss product. Even the smallest defect will jump out and slap you in the face if you use a high-gloss finish. In addition, it will be nearly impossible to keep a high-gloss finish clean; fingerprints, in particular, seem to really stand out in the light. A Semi-gloss, eggshell, or matte finish might be better, especially if there are defects in the paint that you want to hide.
If you don't get any better suggestions (e.g. from Dresdner), your best bet is to put down a de-waxed shellac to seal the paint, then clear coat it with whatever you like. I believe that Zinsser's SealCoat is shellac-based, but I'm not sure about the color. Ideally, you want a "blonde" or "ultra-blonde" shellac, so that it doesn't add any color to the underlying paint.