Trim fat from the chicken breasts and cut into even 2-inch pieces.
In a bowl, whisk together the soy sauce, garlic, ginger, lime juice, and enough of the marinade base to coat the chicken.
Place the chicken pieces and half of the marinade into a resealable bag or container. Refrigerate and marinate 6–8 hours, turning occasionally.
When ready to cook, preheat and clean the grill to medium-high heat. Lightly brush or spray the grill grates with 1 tablespoon avocado oil or another high smoke-point oil.
Stir 1 tablespoon Sriracha into the reserved half of the marinade to make a glaze, and taste to adjust heat.
Drain and discard the marinade from the chicken. Thread the chicken pieces onto skewers, using double skewers or blade-type skewers if available.
Place the skewers on the hot grill and brush generously with the Sriracha glaze. Cook, turning and brushing with more glaze every ~4 minutes.
Grill until the chicken is browned and firm to the touch, about 12–14 minutes total depending on piece thickness, or until an instant-read thermometer registers 165°F (74°C).
Remove from the grill and serve the kabobs hot.