Dredge chicken in 1 cup flour. Heat oil in a Dutch oven to 375°. Add chicken, and fry 20 minutes or until golden brown. Drain.
Melt butter in a heavy saucepan over low heat; add remaining 1/4 cup flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in paprika, salt, and hot sauce. Place chicken on a serving platter, and spoon sauce over the top. Serve warm.