Generally medical professionals do not vouch for using milk for tear gas despite it often being touted. The research seems to suggest they are largely the same in providing relief
Sources to back this up
That means bacteria can contaminate the milk and potentially cause infection if applied to eyes or skin wounds. Jordt says it’s better to use water or saline solutions to wash out eyes after a tear-gas attack
Another source of medical professionals recommending against it
And a study looking at pepper spray as well
In this study, there was no significant difference in pain relief provided by five different treatment regimens. [Water vs milk vs 3 other solutions] Time after exposure appeared to be the best predictor for decrease in pain.
Capsaicin is not water soluble. It is only dissolved in oil or in alcohol. Washing with milk is better than washing with vodka. But water is 100% useless.