Separate calamari rings and place them in a lidded plastic container with enough milk to cover them. Seal the container and allow to soak at room temperature for at least 1 hour.
Heat the oil in a deep fryer.
Combine corn flour and gluten-free all-purpose flour in a shallow pan. Transfer about 6 calamari rings from the milk directly into the flour mixture to coat. Place coated calamari into the hot oil without crowding, and cook until just starting to brown, 2 to 3 minutes per batch. Drain on paper towels. Repeat with remaining calamari.
