Place rack into instant pot (if you are using a slow cooker just put the meat right into the crock). Place the chicken on rack. In a mixing bowl, whisk together bbq sauce, cola, vinegar, and spiced. Pour the bbq mixture over the chicken.
Lock the lid and seal the vent. Set to meat with high pressure for 20 minutes. When it is done allow natural release 10 then finish with manual release.
Remove chicken and place in mixer. Use the paddle attachment and slowly pulse to shred. It is important that you don't cram large of chicken into the mixing bowl because it could damage the mixer or spill hot chicken over the sides.. If you are cooking a larger amount of chicken I recommend that you shred in batches.
Return shredded chicken to the pot. Gently stir and allow chicken to sit in the sauce for a few minutes before serving. If you want the chicken to soak in more flavor from the sauce, set the IP to Keep Warm.
Serve on buns with sliced pickles and pepper jack cheese (or additional sauce if desired).