Preheat the oven to 175 degrees F. Preheat the oil in the deep fryer to 400 degrees F.
For the flour: In a bowl, mix the four, salt and Cajun seasoning.
For the chicken: Toss the chicken with 1/2 cup of the oil, 1 tablespoon salt and 1 teaspoon pepper, and place on parchment paper. Cook slowly in the oven until the chicken reaches an internal temperature of 165 degrees F, about 1 hour. Remove from the oven and cool.
Finally re-season with salt and pepper, and serve.
Airline chicken breasts are boneless, skin-on cuts still attached to the wing up to the first joint.