I had a similar Kodak Chart made for the printing industry. I used it for quick daily calibration of TV cameras.
I notice your chart suffers from a sheen resulting in reflection of the lighting. This results in less color saturation.
One adjustment in post processing might be color temperature. Ideally the RGB samples should only contain each primary color plus an even mix of the other two primaries which affects saturation and brightness. The white, black, and gray chips should have equal amounts of RGB.
You can try running the auto-white balance tool in your post processing editor. Generally it is best to place this tool's eye dropper over a medium gray chip and execute to neutralize any lighting color cast.
There is a free digital download of Munsell\Gretag-MacBeth design chart used for the color checker samples as used by X-Rite. By placing your cursor in your editor over the primary and secondary chips you will see the RGB readout in an information panel or status line to use as a reference.
and download the colorchecker .jpg and the colorchecker data table to see what the readings should look like.
For your Kodak chips the primary and secondary colors should be similar except for the the other two primary colors added in even amounts for luminance and saturation. "White" is even amounts of the RGB components and letus us say a light red not saturated might be 220, 112, 112 in RGB coodinates. In the 220 example, 112 contributes to brightness and 108 remainder to the color portion.
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