During the 12 years I lived in Montana, I trout fished a lot during spring runoff (it starts in mid-May and continues into July depending on the river) when the rivers were chocalate brown in color and well up in the willows. I found the best flies to use in those conditions were large and black, claret, or very dark brown fished on or near the bottom with type 6 or type 8 sinktips or full sinking lines or shooting heads.
Cast upstream and keep the fly under tension as it comes downstream even with you though raising your arms and rod tip (even if that means above your head) to keep slack out of the line and then dropping your arms and rod tip as it goes below you (The late Charlie Brooks wrote about doing this in his books and it was known as the "Brooks Method" for quite awhile). The longer the rod you use, the more line and the longer the cast you can control by raising and dropping the rod tip.
Using this method, I caught many trout between 12" and 5 lbs in the chocalate colored water of runoff.