Preheat grill to medium-high.
Combine coconut aminos, mirin, sesame oil, coconut sugar, ginger and garlic in a medium bowl.
Transfer half the mixture to a small a saucepan and keep the other rest in the bowl so you can add the chicken to toss to coat. Let it marinate, stirring once or twice, for 15 minutes.
Meanwhile, bring the marinade in the mixture in the saucepan to a boil.
Whisk water and cornstarch in a small bowl; add to the saucepan.
Cook, whisking, until the sauce is bubbling and thickened, about 1 minute. Remove from heat and set aside.
Thread mini bell peppers crosswise onto 2 skewers and the chicken onto the remaining 2 skewers.
Oil the grill rack. Grill the chicken, turning occasionally, until an instant-read thermometer inserted in the thickest part registers 165°F, about 10 minutes. Grill the peppers, turning occasionally, until charred, 2 to 3 minutes.
Brush the chicken and peppers with the reserved sauce in saucepan.
Sprinkle with sesame seeds and scallions.