1. Place flour in a shallow dish. Combine milk and egg in a shallow dish, stirring well. Sprinkle chicken evenly with salt. Heat a large skillet over medium-high heat. Add oil to pan; swirl to coat. Dredge chicken in flour; dip in egg mixture. Dredge in flour again, shaking off excess. Add chicken to pan; sauté 3 minutes on each side or until done. Remove chicken from pan using a slotted spoon; drain on paper towels. Combine hot sauce and butter in a medium bowl, stirring with a whisk. Add chicken to hot sauce mixture, tossing to coat evenly. Cut chicken into slices.
2. Combine lettuce, carrot, and celery in a large bowl. Combine buttermilk and remaining ingredients, stirring well. Arrange about 1 1/2 cups salad on each of 4 plates; divide chicken strips among salads. Drizzle dressing evenly over salads.