Separate the chicken wings into drummettes and wings, discarding the wing tip joint. Place chicken wings and drummettes into a large, zip-top plastic bag or large brown paper bag.
In a small bowl, combine the flour, salt, pepper and cayenne. Add the seasoned flour to the plastic bag and toss to coat well.
Pour the chicken pieces and excess flour onto a baking sheet and spread them out evenly. Allow the chicken to sit on the floured baking sheet to dry out for about 1 hour.
In a medium-size saucepan, combine the hot sauce, apple cider vinegar and sugar, and bring to a simmer over medium heat. Reduce the heat to medium-low and cook until the sauce is slightly reduced, about 12-15 minutes.
Using a hand blender, slowly blend in the butter until the mixture is smooth. (The sauce can be served immediately or stored in the refrigerator in an air tight container for several months. The sauce can be reheated over a low heat while constantly whisking to reincorporate the butter.)
Preheat a fryer or a large stockpot filled halfway with vegetable oil to 350°F. Add chicken to hot oil and fry until cooked through and crispy, about 10-13 minutes.
Place the wings in a large bowl and drizzle with half of the sauce. Toss to coat well.
Serve hot with the remaining sauce and blue cheese dipping sauce alongside.