Pour 2 inches of oil in a large Dutch oven (10 quarts or larger) fitted with a deep-fry thermometer and heat to 375 degrees F. Line a baking sheet with a wire cooling rack.
Combine the flour, paprika, salt and cayenne in a large zip-top plastic bag and shake to combine. Pat the chicken wings very dry on paper towels and season lightly with salt. Add half of the wings to the flour mixture and toss to coat. Shake off the excess and add to the hot oil. Repeat with the remaining wings and move the wings around in the oil so they don’t stick together. Adjust the heat so the temperature of the oil stays steady at 350 to 360 degrees F. Fry, turning occasionally, until browned, crisp and cooked through, 12 to 15 minutes, depending on the size of the wings. Drain on the rack and season with salt.
While the wings are frying, carefully melt the butter in a large flame-proof bowl over low heat. Whisk in the hot sauce, BBQ sauce, sriracha and honey. Add the wings. Toss well to coat the wings all over with the sauce.
Transfer the wings to a serving platter and drizzle any sauce left in the bowl over top. Sprinkle with the chopped scallions. Stir together the ranch and blue cheese dressings in a serving bowl and serve with the carrots and celery.