Load the Instant Pot. Place the chicken, olive oil, honey, salt, pepper, smoked paprika, red chili flakes, and garlic powder in the Instant Pot. Stir to coat the chicken thoroughly. Pour the chicken broth over the chicken.
Cook. Seal the Instant Pot and cook on high pressure for 15 minutes followed by a natural release.
Make the hot honey. While the chicken is cooking, combine 1/3 cup honey, apple cider vinegar, and red chili flakes in a saucepan. Bring the mixture to a boil over medium-high heat, whisking continuously. Reduce the heat to low and simmer until the chicken is done and shredded.
Shred the chicken. Transfer the chicken to a cutting board and shred it. Discard the juices left behind in the Instant Pot.
Put it all together. In a large mixing bowl, combine the shredded chicken and hot honey. Toss to coat the chicken.
Assemble the sandwiches. Spread the mayonnaise over both sides of each bun and divide the chicken between the buns. Top the chicken with pickles and close the sandwiches.
Notes
Any leftover spicy chicken should be stored in an airtight container for up to 5 days with the cooking liquid for the best results to keep the chicken from drying out for the next time you want to enjoy a spicy chicken sandwich.