Pour 2 quarts vegetable oil into a large, heavy pot and heat to 350°F (use a deep-fry thermometer). Line a platter with a few layers of paper towels and set near the stove for draining fried pickles.
Drain 16 ounces dill pickle chips in a colander to remove excess brine. Transfer the drained pickles to a medium bowl and pour 2 cups buttermilk over them so they are covered; set aside while you prepare the coating.
In a separate large bowl, stir together 2 cups whole-wheat flour, 1 cup all-purpose flour, 2 teaspoons salt, 1 teaspoon paprika, and 1/4 teaspoon cayenne pepper until evenly combined.
Working in small batches, use tongs or a fork to lift a handful of pickle chips from the buttermilk, letting excess buttermilk drip back into the bowl for a moment.
Dredge the pickles in the seasoned flour mixture, coating each piece completely. Shake off excess flour so the coating is not clumpy.
Carefully place the coated pickles into the hot oil in a single layer, being careful not to overcrowd the pot (fry in batches as needed). Maintain the oil temperature near 350°F; reduce heat if it rises too high.
Fry the pickles until golden brown and crisp, about 1–3 minutes per batch (times may vary by pot and stove). Use a slotted spoon to remove the fried pickles.
Transfer the fried pickles to the paper-towel–lined platter to drain. Repeat steps 4–7 with the remaining pickles and coating until all are fried.
Let the fried pickles drain briefly on the platter, then serve warm.