Place toothpicks in a small bowl and cover with water; let them soak to keep them from burning while cooking.

Mix 2 teaspoons chili powder and 2 teaspoons cumin in a shallow dish.

Preheat an air fryer to 400 degrees F (200 degrees C).

Place chicken breast on a flat work surface. Slice horizontally through the middle. Pound each half using a kitchen mallet or rolling pin until about 1/4-inch thick.

Sprinkle each breast half equally with remaining chili powder, remaining cumin, chipotle flakes, oregano, salt, and pepper. Place 1/2 the bell pepper, onion, and jalapeno in the center of 1 breast half. Roll the chicken from the tapered end upward and use 2 toothpicks to secure. Repeat with other breast, spices, and vegetables and secure with remaining toothpicks. Roll each roll-up in the chili-cumin mixture in the shallow dish while drizzling with olive oil until evenly covered.

Place roll-ups in the air-fryer basket with the toothpick side facing up. Set timer for 6 minutes.

Turn roll-ups over. Continue cooking in the air fryer until juices run clear and an instant-read thermometer inserted into the center reads at least 165 degrees F (74 degrees C), about 5 minutes more.

Drizzle lime juice evenly on roll-ups before serving.