There are all sorts of things I have found around the interwebs but nothing that I have found seems to fit this issue. Our home has a partial second story so there are a variety of levels of roof. This creates a couple spaces with short sections of gutter. There is one section on the SE corner of the house, facing ESE, about 10ft long, and it vibrates in high winds. Usually it is intermittent, but with the storms the last 24 hours it has been nearly constant. The wind is coming out of east, which doesn't happen too often here, at least not sustained. I can only get to it from the roof, as I do not have a ladder tall enough to reach in that part of the house.
I went out this AM when the wind was making it go nuts and it appears as if the problem is flashing vibrating against the inside of the gutter. The downspout is secure and does not transmit much vibration at all. The gutter itself is solidly attached from what I can tell. When I hold the gutter or downspout to dampen the noise, it continues. When I push the flashing back against the gutter (maybe a 1/8" to 1/4" gap?) the noise either stops or abates. When I just feel that flashing when it is vibrating, I am 95% sure that is what is vibrating and making the noise.
Any ideas on how to brace/prevent the flashing from vibrating or otherwise dampen that noise?
Thanks!

 

You could probably put a few screws through both to suck them together (such as neoprene washer barn screws).

 

You can add more support to the gutter. You can also try altering the aerodynamics around the problem gutter. Sometimes just a little ridge, fin or other protuberance is all that's needed to disturb the air flow and stop the harmonic.