In The Road, in a flashback, the wife is looking out the window to witness fire when the husband starts running bath water. Why does he do this?

The scene that you are describing is when the first chaos is occurring that eventually leads to the mass destruction of mankind.  Both the wife and her husband didn't really know what was going on; they were confused and a bit alarmed.  They got out of bed, and tried turning the lights on, but they didn't turn on; the electricity was already gone.  The father, realizing that they didn't have power, probably wondered if the water lines were damaged, or if the pipes had been hit.  So, he went to the bathtub and turned on the faucets "on both taps as far as they would go."  He was probably just checking to see if they still had functioning water.  Why?  The power was off, they had seen fire and heard rattling like a bomb or a major impact of something, so he was probably worried that the damage was more extensive than just the power.

It never directly states any of this in the novel--this is one of those situations where you have to infer, or use an educated guess to read in-between the lines.  It only makes sense that the father would be concerned about their safety and resources.  His wife, confused, asks, "Why are you taking a bath?" and he says that he isn't, and that is all that the book tells us, so inference is the way to kind-of guess what he might be doing. I hope that helped; good luck!