Soaking the chicken. Using a large bowl, soak all the chicken pieces in the buttermilk. Let them marinate overnight. The next day, remove the chicken pieces from the buttermilk. Pat them dry with paper towels. Season all the pieces with salt and pepper, coating all the sides.
Preparing the oil. Put a 12-inch skillet on the stove. Add the canola oil, which should come up to 1/2-inch deep in the skillet. Turn the burner on high and heat the oil until it is 350 degrees F.
Coating the chicken. Whisk the eggs and milk together until combined. Set up the breading station: a saucer with the sorghum and rice flours combined, a bowl with the egg mixture, and a saucer with the gluten-free bread crumbs. With your left hand, dredge a chicken piece in the flour mixture to coat evenly. Shake off the excess flour. Dunk the chicken piece into the egg mixture with your left hand. Coat the chicken in the egg mixture, using your right hand, until it is thoroughly coated. Remove the chicken and place it onto the saucer with the bread crumbs. With your left hand, coat the chicken with the bread crumbs. This way, your left hand stays dry, and your right hand will be the wet hand. Repeat this with all the chicken pieces and place them on a waiting plate.
Frying the chicken. Once the oil is 350 degrees F on your thermometer, carefully add the chicken pieces into the skillet and turn the heat down to medium-high. Cook the chicken until the side that is in the oil is browned, which should be about 5 minutes. Turn the chicken pieces over. At this point, the oil should be maintained at 250 to 300 degrees F. If the oil dips below that temperature, turn the heat to high. Cook for another 10 to 12 minutes, or until the breast pieces reach an internal temperature of 160 degrees F and the legs reach an internal temperature of 180 degrees as noted on a meat thermometer.
Finishing the chicken. Put a wire rack above a large pan. Take out the chicken pieces from the skillet and place them on the wire rack, allowing the excess grease to drain into the pan below. Eat the chicken with delight.