What gives diarrhoea caused by Cholera its milky colour?
The color of our feces is caused by the breakdown products of the hemoglobin, namely Bilirubin and Stercobilin, which depending on the concentration, cause a yellow to brown color. See here for details.

Since the amount of liquid lost by the cholera diarrhea with up to 250ml/kg bodyweight is really high, there is only very little to nothing of these breakdown products available in the feces. This causes an absence of color.