1. Preheat oven to 375°.
2. Line an 8-inch square metal baking pan with foil, allowing foil to extend over edge of pan; coat foil with cooking spray.
3. Weigh or lightly spoon brown rice flour, potato starch, and tapioca flour into dry measuring cups; level with a knife. Place brown rice flour, potato starch, tapioca flour, 1/4 cup coconut, walnuts, and next 4 ingredients (through salt) in a food processor; pulse 2 times or until blended. Add butter; process until mixture resembles fine meal.
4. Reserve 1/4 cup flour mixture. Firmly press remaining flour mixture into bottom of prepared pan. Spoon cherry preserves over crust, spreading evenly. Combine reserved 1/4 cup flour mixture and 1/2 cup coconut; sprinkle over cherry preserves. Bake at 375° for 20 minutes or until bubbly and top is lightly browned. Cool completely in pan on a wire rack.
5. Lift bars from pan, using foil sides as handles. Place on a cutting board; cut into 16 squares. Remove from foil.