There is not one single plating thickness per layer that is used universally. I can tell you the chromium layer is usually very thin, compared to the nickel layer. I'm guessing it would not be more than 10 microns. It would be nice if it could be learned if the original plating was done to a standard industry specification, as is usually the case today. Then you could fairly easily duplicate it. I think it is unlikely, though.
These days platers have a range of standard thicknesses they apply to meet different specifications and they can control those thicknesses well.
I suggest you contact a plating shop there, where you live. They should be able to help you. It could be more effective for you to compare plating samples to your Leica than to determine your exact plating thicknesses through other methods. If necessary, they could plate some test pieces of brass for direct visual comparison. An experienced plater might have a good idea of thicknesses, just from examining the finish.
But thickness is not everything. Electroplated nickel can vary in color significantly from a dull gray to a color resembling stainless steel. So, I would expect the specific plating information you now have to be of help to the plater to replicate the original color of the nickel interlayer.
Also, something to consider: The older chrome processes usually used hexavalent chromium which is very toxic. Trivalent Chromium is less toxic and more common today, though hexavalent is still used. The trivalent is easier, and less expensive for the plater to use. It throws better, meaning it forms a more uniform layer, especially on inside corners or on intricate shapes. But its color is different. From what I understand, platers can modify trivalent chrome with additives to make it look like hexavalent chrome.
An electron microscope could be used to determine thicknesses, if you have access to one. Even with that information, it will take some experimentation to replicate the original Leica finish.
Also understand that as a satin chrome piece is handled over time, it will look a little more shiny, as handling polishes the "peaks" while leaving the "valleys" the original finish. So to truly replicate an original satin chrome finish, the sample of the original finish must be an area that gets little contact.
One last idea: maybe you could find someone who specializes in restoring old Leicas, who might already have the information you need, or have the ability to replicate the original finish.