Mix the milk and 4 teaspoons of the salt in a large bowl. Pat the chicken dry. Add the chicken to the milk mixture, cover, and refrigerate for 8 to 10 hours.
In a shallow dish or on a plate, combine the flour, smashed cereal, saltines, remaining teaspoon of salt, mango powder if using, and cayenne. Beat the eggs in a shallow bowl. Remove the chicken from the fridge.
Place a deep, heavy pan over medium-low heat. Pour in the oil and, if using, the butter. If using oil and butter, use only 1 1/2 cups oil. If using only oil and no butter, use 3 cups. Heat it over medium-low heat until it registers 350°F (176°C) on a deep-fry or candy thermometer.
Dredge each piece of chicken first in the flour mixture, then in the beaten egg, then in the flour mixture again, rolling to coat each time.
Fry the chicken, working in batches, on medium-low heat until golden and crisp, 7 to 10 minutes on each side (7 minutes for wings, 10 minutes for breasts). Don’t crowd the pan—cook just enough pieces at a time so that each is bathed in oil. Keep a careful eye on the flame, as the butter will turn brown before the chicken is properly cooked if the heat gets even a smidgen too high.
Check the chicken for doneness. If the chicken isn't quite done, transfer it to a wire rack placed on a baking sheet, slide it into the oven, crank the heat to 400°F (204°C), and come back for the chicken after 12 or so minutes. Slip a sharp knife into the deepest portion of 1 piece of chicken just to be sure it's done.
Drain the chicken on a brown paper bag. Resist the urge to consume it straightaway and instead wait for it to cool at least 5 minutes. Don't worry, the coating will remain crisp and you'll be able to better appreciate the slight sweetness from the saltines. Serve with lotsa napkins.