I think you will want to do some more paint research and experiments. Most acrylic paints can scratch and flake very easily. This can depend a lot on the texture of the painted surface. More texture equals a better bind. Applying a clear coat sealer prior to engraving may be an option. Ideally you will use an air brush with masking on the chip to get an even coat. An uneven coat will flake during engraving I think.
You may want to consider a modeling enamel. Be aware that a lacquer can be an attractive choice because it is so much more durable (used as automotive paint) BUT it can melt many plastic types. I am not sure how it would react to a clay composite. Both enamel and lacquers are more of a pain to use becasue they need solvents to clean up, require string ventilation when using and have a strong odor.
I would speak to somebody at a really good model shop if you have one in the area. This page has a good paint for model work overview:
http://www.scalemodelguide.com/painting-weathering/painting-guide/paint-types/