As potassium chlorate is an ionic compound, it's obvious that it dissolves in ionic solvents. Moreover, it is hygroscopic and can't be stored in water. Are there any solvents in which it does not dissolve and with which it won't react?
I should think that any non-polar organic solvent highly resistant to oxidation would do the trick. I assume you wish to make a suspension. Have you tried nujol (mineral oil) or simply a higher molar mass alkane? By ionic solvent I assume you mean polar solvent.
Mr. James Falcone, Jr., assuming that KClO3 is stored in an organic solvent, how to take it out? Could basic filtration suffice this? Moreover, could you please name some commercial organic solvents resistant to oxidation?
As I have already suggested..have you tried suspending it in nujol...simple mineral oil? I have no idea of what you plan to do with it post-storage, but off the top of my head if I needed it after storage I would simply vacuum filter it. This would likely leave some solvent residue which could be displaced (washed off) with a more volatile non-polar aprotic solvent. Please consult simple references ...you might start here:
I would not suggest to store it in any organic solvent which anyhow could be oxidized and/or combusted. Also, mixtures with potassium chlorate are known to be explosive.
See http://www.sigmaaldrich.com/MSDS/MSDS/DisplayMSDSPage.do?country=EN&language=en&productNumber=P1338&brand=SIAL
If you want to really store it for a longer time, use (ultra)high-vacuum for the solid. Then it stays pure and water-free (at least for a reasonable amount of time).