Something based on a vibrating sander, gives the correct motion. $5 at a million
yard sales.
Or, attach a small electric drill to the side of the sifter. It
should contain a bit maybe 6 inches long. Tape a nut, bolt or coin to the drill bit. Now it's out of balance and will shake when you squeeze the trigger. I sifted soil this way and made a
thread, I think.
You can rig up the drill in about a minute, then holding both the drill and sifter of flour, test it. Use a variable speed drill and start slowly. Start with something quite light taped to the bit. Go heavier for more shake. This absolutely will work.
Edit
https://permies.com/t/12414/Nature-powered-gravel-washing-station
FOUND IT !!! I Googled my name with "electric drill screener, permies Dale Hodgins " and a 2012 thread came up. It references and 2011 thread. ..... Sometimes I have an idea, Google it and there I am, pontificating on that very thing, years earlier.
........
This is something I gleaned from one of my posts in green building ------------------ POWER SCREENER------------I've invented a dead simple power screener. I'm sure this has been invented before but it worked so well I'm going to tell you about it anyway.----------- I needed to screen rocks out of some reasonably dry dirt. I had a big screen about 4 ft. in all dimensions. I found that it worked reasonably well when used on a slope with only gravity powering it but I wanted to make it process material quickly and to break up lumps.
I mounted an electric drill to the top of the screen. I used duct tape to attach a bolt to the side of a drill bit so that it was seriously out of balance. With the trigger locked in the "on" position, the drill vibrated wildly and transferred that
energy to the screen.
No doubt this is hard on electrical equipment. But there are plenty of old drills and skill saws which have no value. Any of these items may be altered so that they shake a great deal. They could be used for processing earthen plasters, for soil sifting, etc.