Slice the chicken breast into even 1-inch wide strips or tenders.
Place chicken in a bowl and pour the buttermilk over it, ensuring every piece is coated; let marinate for at least 15 minutes.
In a shallow dish, whisk together the almond flour, arrowroot starch, garlic powder, onion powder, smoked paprika, sea salt, and black pepper.
Remove each piece of chicken from the buttermilk, letting excess drip off, then dredge thoroughly in the flour mixture until fully coated.
Preheat the air fryer to 390°F and lightly coat the basket with avocado oil.
Place the chicken in a single layer in the basket, spray the tops lightly with avocado oil, and cook for 10-12 minutes, flipping halfway through, until the crust is golden and the chicken is cooked through.
While the chicken cooks, toss the shredded cabbage with apple cider vinegar in a small bowl to serve as a bright, acidic side.