Wash and pat chicken thighs dry. Pour jerk seasoning over the the chicken and combine, making sure that all the chicken thighs are covered with the seasoning.
Set Instant Pot to sauté, select more so that the sauté setting will be on high heat.
Once Instant Pot says hot, add vegetable oil. Place 2-3 pieces of chicken in the Instant Pot. Cook each side until browned (about 2 minutes per side). Cook in batches until all chicken thigh pieces have been browned. Set to the side.
Once all chicken pieces are removed, add about ¼ cup chicken broth to the bottom of the Instant Pot. Use a wooden spoon to get up all of the brown bits on the bottom.
Add yellow onion, green pepper, minced garlic, and green onions. Stir until onions are softened, about 3 minutes. Turn off Instant Pot. Add sweet potato, red kidney beans, corn, and chicken broth. Place browned chicken thighs on top of the soup, ensuring that the chicken thighs are in the liquid. Cover and cook on high pressure for 15 minutes.
Once pressure cook cycle is complete, allow soup to natural release for 10 minutes, then release the remaing pressure. Once all pressure is released, open lid and stir, shredding the chicken as you stir. Add coconut milk. Season with salt and pepper and top with cilantro.