Trim chicken of excess fat and lightly score the skin side with a sharp knife. This will help the flour to stick.
Lightly season the chicken with the pepper and transfer it to a zip-top bag set in a bowl to catch any drips. Pour in the dill pickle juice, seal the bag and refrigerate overnight.
When ready to cook, place the cassava flour, arrowroot starch, and eggs into three separate bowls. Season the cassava flour and arrowroot starch with ¼ teaspoon salt each. Add the hot sauce and water to the eggs and whisk vigorously until frothy.
Dredge each piece of chicken in the arrowroot starch, then dip into the egg wash, and finally dredge in the cassava flour.
Heat a 10-inch non-stick skillet over medium-high heat. Add the avocado oil and heat for 1 to 2 minutes, until it shimmers. Working in batches, carefully add the breaded chicken, scored side-up at first, to the hot oil and cook until golden brown, about 5 minutes. Flip and cook for an additional 4 minutes, or until the thickest part registers 185F on an instant read thermometer.
Transfer the fried chicken to the cooling rack. Lightly season with a pinch of salt and serve with hot sauce, Dill Pickle Mayo, if desired, and lemon wedges.