Mix the salt, pepper, cayenne pepper, garlic powder, onion powder and dry mustard powder together in a bowl. Divide the spices evenly between 2 mixing bowls.
Add the flour to 1 of the bowls, mix well, and set aside.
Rub the chicken drumsticks with the reserved spice mix. Poke all of the pieces with a fork a few times to let the flavors seep down into the meat. Set aside.
Pour the buttermilk over the chicken, and cover the bowl with plastic wrap. Refrigerate for at least 1 hour. You can also let the chicken marinate longer, even overnight.
Add the flour mixture to a large re-sealable plastic bag. Remove the chicken pieces from the buttermilk and in batches, drop them into the bag, shaking them to make sure they become heavily coated.
In a large heavy-bottomed saucepan, pour enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 360 degrees F. (If you don't have a thermometer, a cube of bread will brown in about 3 minutes.).
Drop the coated chicken drumsticks into the hot oil. Turn the pieces as they brown and do not let them touch each other while frying. Work in batches, if necessary check the underside of a piece by lifting it with tongs. It should be a deep golden brown.
Cook the chicken until the pieces are crispy and brown, about 15 minutes, turning occasionally. To test for doneness: Cut into the thickest part of a drumstick. The juices should run clear and the meat should be opaque throughout. If necessary, pop the chicken into a preheated 325 degrees F oven, until they are fully cooked.
Transfer the fried chicken to a paper towel-lined baking sheet to drain the excess oil. Transfer the drumsticks onto a serving platter, or put into a bucket. Serve the chicken hot, room temperature, or cold.