Place 1 cup flour in a bowl; mix in ranch dressing.
Split chicken breasts to create 4 pieces. Coat each piece with plain flour, dip in egg, and coat with flour-ranch mixture. Place on a wire rack set over a rimmed baking sheet.
Heat oil in a large saucepan until almost boiling. Add 2 pieces chicken; fry until lightly golden, turning once, about 5 minutes. Return chicken to the wire rack. Repeat with remaining 2 pieces chicken.
Bake chicken in the preheated oven until juices run clear, about 10 minutes.
Mix mayonnaise and sriracha sauce together in a small bowl. Spread on rolls. Place 4 pickle slices on each roll. Place 1 piece of chicken on each sandwich.