Forest fires and water quality

It would affect water quality as soon as there was rain. It would be noticeable downstream at the flow rate of the river, probably about five miles an hour, but the effect would diminish with every mile as water from other sources entered the river. There certainly would be some evidence of the deforestation 50 miles downstream, but there probably would be negligible effect 500 miles downstream. There are many factors that would come into play, but you're writing fiction, so make it the way you want it to be.

PeterL is correct. However, controlled burns don't usually cause large-scale erosion. Catastrophic wildfires and clear-cutting (especially if heavy equipment is used), however, are much more ecologically damaging.

The problem is soil erosion and siltation after such an event. Fish kills would not result unless you have a very silt-sensitive species (trout, perhaps?). The fish kills I am familiar with are usually due to mass release of a pollutant, a disease outbreak, a very hard freeze (most notably in ponds rather than rivers), the water getting too hot (which could be due to loss of tree cover) or a massive release of sewage that depletes the dissolved oxygen in the water. Play with some of those ideas. I think you can use any of them with little trouble.