I found this thread searching for the very same answer. This thread was so helpful in giving me ideas I thought I'd share what worked for me on separating dock seeds from the chaff:
Get some aluminum window screen from the hardware store. (Fiberglass screen is what most modern window screens are made of and I think it's too flimsy for this project, but maybe you can get it to work). Staple TWO LAYERS of this screen very tightly across a rectangular wooden frame. You want the screen taught enough so that the two screen layers are lying right next to each other. Note the point of doubling the screen thickness is to make the gap or holes in the screen effectively smaller (when layered) so, make sure the holes in the two layers are offset from each other when stapling.
Place this frame over a pan, cookie sheet, the ground--or wherever you want to catch the chaff. Now take 1/4 cup of VERY DRY dock seeds and put them in the middle of the screen frame. Rub the seeds back and forth across the screen with your fingers. Very quickly the chaff will fall through the gaps in the screen leaving the seeds on top. Brush the seeds off the top of the frame into a dish or bag. Voila! Separated seeds!
You might need to experiment with the dock seeds from your particular part of the world (or the screen size from your particular hardware store). In my climate (mountain, high desert) the dock seeds are quite small and fall through the gaps in the screen along with the chaff unless I double-layer the screen. ...But even in that case (a single layer screen), the seeds that fall through are easily recovered by winnowing as described by Jon above. The rubbing of the seeds on the screen turns the chaff into a very fine dust which is easily blown away.
Good luck!
