Preheat an air fryer to 350 degrees F (175 degrees C). Grease 2 individual ramekins.
Combine chocolate chips and butter in a microwave-safe bowl. Microwave on high for 1 minute. Stir and microwave at 15-second intervals until almost melted. Remove from the microwave and stir until chocolate is completely melted and thoroughly combined.
Mix powdered sugar, egg, egg yolk, vanilla extract, and salt into the melted chocolate; whisk until combined. Add flour and mix until incorporated. Pour batter into the prepared ramekins and place into the air fryer basket. Cover the ramekins with large pieces of foil, tucking ends underneath to prevent foil from flying off.
Cook for 8 to 10 minutes. Remove foil and continue cooking until edges are set, an additional 2 to 4 minutes. Remove from the air fryer and let sit for 5 minutes.
Invert onto dessert plates and serve immediately.