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the only time I ever need to clean a stone is if I'm using light pressure large surface area application such as deburring dings from a machine tool table or grinding large flats. ninety-nine percent of the time, the EDM Stone breaks down into a slurry and that slurry does the cutting. The stone itself never needs to be cleaned, it is friable and breaks down in use. if you are running into a problem in normal use, you might not be using the right stone?
I use falcon tool diamond thinner not kerosene. I don't know if that makes a difference or not. I know you can use WD-40 in a pinch, but it's not great and it does get gummy as it dries. Kerosene may be similar.
Might need a softer stone too, if it's a large area and modest pressure. I think that could clog and glaze a stone.