Separate the onion rings and place into a shallow bowl or baking dish. Cover with buttermilk pushing the rings down into the liquid while you get everything else ready to go.
Whisk together mayonnaise, ketchup, horseradish, paprika and oregano. Season with some of the salt and pepper. Stir in as much hot sauce as you like. Pour the dipping sauce into a bowl.
Whisk together 1 cup all-purpose flour with 1 cup rice flour in a shallow bowl or baking dish. Stir in the club soda and beer.
Place the remaining 2 cups all-purpose flour into a shallow baking dish. Whisk in chili powder and season generously with salt and pepper.
Heat about 3-inches of vegetable oil in a deep, large pot over medium-high heat to 350°. The vegetable oil should come no higher than one third up the side of the pot. Once you add the onion rings, the oil will bubble up. The temperature of the oil will go down when you add battered onion rings and then come up again as they cook. I use a candy thermometer to make sure that the temperature is hot before I add more onion rings to the oil.
Lift an onion ring out of the buttermilk and shake off the extra liquid. Dredge into the seasoned flour and then dip into the beer batter, again shaking off the excess liquid. Place the battered onion ring into the hot oil. Continue this process to fry several rings at a time, being careful not to place too many into the oil at the same time. You want them to swim freely as they fry. Use a slotted spoon or spider strainer to turn the rings in the oil until golden brown on both sides, about 3 to 5 minutes. Remove the rings to a paper towel lined baking sheet.
Continue with the remaining rings until there are none left. Once you remove the onion rings from the oil, immediately sprinkle with parsley and flakey salt.
Serve with dipping sauce.