I can't answer you definitively, but I think you will not be able to engrave chrome with a CO2 laser. A YAG or a fiber laser may work. Take it to a good shop in your area and they should be able to see what would work for you.
Your designs can be VERY intricate, and the edges should be clean cut and avoid flaking. That said, you won't know until you try! Can you get a sample of the substrate and coating you will be using as a sample and have a shop work with that to test what is possible?