Add chicken strips to a shallow dish then cover with buttermilk and refrigerate for 15 minutes. Meanwhile, pulverize Rice Chex in a food processor until very fine then pour into another shallow baking dish (omit this step if using regular bread crumbs.) Add spices, salt through cayenne pepper, to the crumbs then mix well to combine and set aside.
Setup a breading station for the chicken fingers: dish with chicken, dish with seasoned crumbs, and a foil-lined baking sheet. Working in batches, remove chicken fingers from buttermilk, shaking excess off, then roll in seasoned crumbs until well coated, and then place on baking sheet. Continue with remaining chicken strips then refrigerate for 10 minutes to help set the breading (if time is of the essence you can skip the refrigerating step.)
Pour 1" oil in a large cast iron or heavy-bottomed skillet over medium heat then heat until hot (see notes for checking oil temperature.) Add 4-6 chicken fingers to the oil, being carful not to overcrowd the pan. Turn heat up slightly if necessary to compensate for adding the cold chicken then turn the heat back down once its comes back up to temperature. Fry chicken until golden brown on one side then flip and fry until golden brown on the other - 1-2 minutes per side. Remove to a paper towel lined baking sheet then continue with remaining chicken fingers.
Notes
Test to see if the oil is properly heated by dropping a few pieces of the breading mixture into the oil. If it sinks or stays in the middle and has very few bubbles, the oil is too cold. When it stays on the surface and bubbles consistently but not ferociously, the oil is hot enough.