For the meatballs: Place the chicken thighs, eggs, celery salt, and white pepper in a food processor. Pulse until the meat is ground but still a little bit chunky. Do not make a smooth paste!
Transfer the chicken mixture to a bowl. Stir together the breadcrumbs and blue cheese until combined.
Fill a small bowl with water. To form the meatballs, wet your hands a little and shape the mixture into 1-inch balls. Lay the meatballs on a sheet tray.
Heat a large, deep pan over medium-high heat and add the oil to fill about 1/4-inch up the sides. Do not fill the pan completely with oil.
Pour the flour into a shallow dish and season with salt and pepper. Roll each meatball in the flour to give it a light coating.
When the oil is hot, add the meatballs and cook until golden brown and cooked through, about 10 minutes. Flip the meatballs halfway through cooking. You may have to cook them in batches if they don't fit in the pan, adding more oil if needed. Drain the cooked meatballs on a paper towel-lined plate.
For the sauce: Combine the tomato juice, rice wine vinegar, hot sauce, celery salt, white pepper, and salt in a large bowl. Whisk in the oil until well blended and slightly thickened.
For serving: Transfer half the meatballs to a large bowl. Pour some of the sauce over top, just enough to coat the meatballs. Gently toss the meatballs around to coat in the sauce. Using tongs, transfer the meatballs to serving plate and insert a toothpick. Repeat with remaining meatballs.
Pour the remaining sauce into a small bowl and serve as a dipping sauce.