For the marinade: Place a chicken thigh on a cutting board, cover with plastic wrap, and gently pound to even out the thickness. Sprinkle with salt and pepper on both sides and place in a bowl or resealable bag. Repeat with remaining thighs. Add the Jamaican jerk sauce and mix to coat the chicken evenly. Let marinate at room temperature for 2 hours.
For the rice: Add the rice, chicken stock, Jamaican jerk sauce, red pepper flakes, garlic, thyme, a pinch of salt and a few grinds of black pepper to a rice cooker. Cook rice according to rice cooker instructions.
For the skewers: Heat a grill pan over medium-high heat. Thread 2 skewers on either edge of a chicken thigh, then add an onion followed by another thigh (so the chicken and onions lay flat, not stacked). Repeat with remaining chicken and onions. Place skewers on grill pan and cook 5 minutes, then flip, brush with Jamaican jerk sauce and dome with a large metal bowl. Cook on second side until chicken is cooked through, 4 to 5 minutes. Remove to a plate to cool slightly before removing skewers.
To serve: Chop the onions. Fluff rice and stir in onions and chopped parsley. Serve with chicken.