I don’t think the drinking water disinfectants are likely to have an appreciable effect on high-potency probiotics like VSL. The probiotic concentrations are very high, the gut environment has lots more going on than tap water, and the chlorine concentrations are pretty low. VSL may work a bit better mixed in yogurt than tap water, but that’s probably more about the yogurt than the water.
You could filter your drinking water, e.g. with a Brita filter. That will remove the chlorine.