Preheat the air fryer to 400°F (about 200°C) for 10 minutes.
Trim and pat the chicken breasts dry, then cut into roughly 1-inch nugget pieces. Place in a bowl and toss with a pinch of sea salt and 1 teaspoon sesame oil until evenly coated.
Combine 1/4 cup coconut flour and 1/2 teaspoon ground ginger in a large resealable bag or shallow bowl. Add the chicken pieces and shake or toss to coat each piece in the coconut flour mixture.
Place the 4 egg whites in a separate bowl and add the flour-coated chicken, tossing so each piece is well coated in egg.
Put the 6 tablespoons toasted sesame seeds in another resealable bag. Shake excess egg off each piece, add the nuggets to the sesame seed bag, and shake until evenly coated with seeds.
Spray the air-fryer basket mesh generously with cooking spray. Arrange the coated nuggets in a single layer without crowding; spray the tops lightly with cooking spray.
Cook in the air fryer for 6 minutes. Turn each nugget, spray again with cooking spray, then continue cooking for an additional 5–6 minutes until the nuggets are cooked through and no longer pink inside (internal temperature 165°F).
While the nuggets cook, whisk together 2 tablespoons almond butter, 4 teaspoons coconut aminos, 1 tablespoon water, 2 teaspoons rice vinegar, 1 teaspoon sriracha, 1/2 teaspoon ground ginger, and 1/2 teaspoon monk fruit (if using) in a medium bowl until smooth.
Serve the hot chicken nuggets with the almond-coconut dipping sauce.
