Seems maybe to come originally from some guy’s interpretation of an Arab interpretation of the passage, which replaces water with milk but equates the blood part to “blood of the covenant”:

H.C. Trumbull contrasts the expression with a comparison of blood and milk in the Arab world:

We, in the West, are accustomed to say that “blood is thicker than water”; but the Arabs have the idea that blood is thicker than milk, than a mother’s milk. With them, any two children nourished at the same breast are called “milk-brothers,” or “sucking brothers”; and the tie between such is very strong. […] But the Arabs hold that brothers in the covenant of blood are closer than brothers at a common breast; that those who have tasted each other’s blood are in a surer covenant than those who have tasted the same milk together; that “blood-lickers,” as the blood-brothers are sometimes called, are more truly one than “milk-brothers,” or “sucking brothers”; that, indeed, blood is thicker than milk, as well as thicker than water.[16]

(From the Other Interpretations section)