I tore down a dirted tank about a year back. I spread the dirt/flourite mix over a few buckets/bins, so it was only about an 1" or two thick, and let it dry out.
Whenever I did a water change (new setup), I'd pour the water into one of the bins, stir it up good with a spoon, and then pour off the water and floaties.
It took several cycles, but eventually I got pretty much clean flourite.
I imagine it would work with sand as well, but it will probably take more cycles.