Add enough vegetable oil to a high-sided skillet to go up the side about an inch. Place over medium heat and bring the temperature up to 350°F. If you don't have a thermometer, place the handle-end of a wooden spoon in the oil. If tiny bubbles appear around the handle, you're there.
While the oil is heating up, place the flour in a shallow baking dish and add the dry mustard, paprika, garlic powder, salt and freshly ground black pepper. Mix thoroughly to combine.
Place the buttermilk in a second baking dish. Dip the chicken tenders into the flour, shaking off any excess. Dip into the buttermilk and coat. Dip back into the flour, then the buttermilk and then give it a final dip in the flour.