How can I stop gutter water flow noise?
The sound should be the water entering the downspout's top, but could also transmit from the water hitting the very bottom elbow at the ground. One solution is to remove a few gutter nails or screws back from the window &amp; install rubber bushings or pads to insulate or isolate the gutter's connection to the house. Then, of course put your gutter screws or nails back in...a little loose will assist the padding.

A Second measure, is to back the gutter &amp; downspout, give them more density. Like a stainless steel kitchen sink's noise reduction pad(s). As an example is Grace's Vycor Plus Ice &amp; Water Shield self-adhesive flashing. The 4" wide by 75' long for $20 at home improvement stores should accomplish this quite well. You can build it up to dramatically deaden or eliminate that sound &amp; then paint it to match.