Mix flour, 2 teaspoons of kosher salt, and 1 teaspoon of ground black pepper in a bowl or resealable plastic bag. Coat turkey legs thoroughly in the mixture, pressing the coating. Allow to stand at room temperature while oil heats.

Heat oil in a saucepan or deep skillet to 350°F (175°C). Combine the remaining salt, pepper, paprika, garlic powder, cayenne, and brown sugar in a medium bowl until evenly blended; set aside.

Fry turkey legs, 2 at a time, until an instant-read thermometer inserted near the center reads 170°F (77°C), about 15 minutes. Drain on a wire rack set over paper towels.