Cut chicken into uniform 1-inch nugget pieces and place in a bowl with pickle juice to brine for 10 minutes.
In the first shallow bowl, mix tapioca flour with garlic powder, onion powder, paprika, garlic salt, dried oregano, and cayenne.
Beat the eggs in a second shallow bowl.
Combine the gluten-free panko and grated Parmesan in a third shallow bowl.
Drain chicken and pat dry. Dredge each piece in the seasoned tapioca flour, dip in beaten egg, then press firmly into the panko-Parmesan mixture to coat.
Arrange coated nuggets in a single layer in the air fryer basket without touching.
Spray all sides generously with oil for even browning and crisping.
Air fry at 400°F for 12 minutes, flipping halfway through (at 6 minutes).
Check that the thickest piece reaches 165°F on a meat thermometer before serving.
Let nuggets rest 2 minutes so the coating sets and stays crisp.