Check out the -color-matrix operator to see if it meets your needs.

From your description, I think the following RGB matrix transform will work:

 0  0  1   (R =  B)
 1  0 -1   (G =  R - B)
 0  1 -1   (B =  G - B)

But from the graphic in your post, it looks like the following RGB matrix transform is what you're after:

0    0     1      (R = B)
0.8  0    -0.8    (G = 0.8*R - 0.8*B = 0.8 * (R - B))
0    0.96 -0.96   (B = 0.96*G - 0.96*B = 0.96 * (G - B))

So your command would look like (using the 2nd matrix, for example):

magick <input_file> -color-matrix ` 0    0     1
                                    0.8 -0.8   0
                                    0    0.96 -0.96 ` <output_file>

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Note that color channels are non-negative. Because you are subtracting channels, you might need to make sure your resulting values are non-negative as well, by adding a constant offset for the channels that had subtraction. The color matrix can accommodate 3 additional columns: 'Black', 'Alpha', and Constant, in that order. I assume your Black and Alpha channels are zero. In order to specify Constant, you have to specify '0' for Black and Alpha. So the final matrix might look like:

0    0     1     0  0  0     (R = B)
0.8  0    -0.8   0  0  0.8   (G = 0.8R - 0.8B + 0.8)
0    0.96 -0.96  0  0  0.96  (B = 0.96G - 0.96B + 0.96)

You'll have to experiment to see if you need to specify the constant value.