Pat chicken breast dry and season with salt and pepper. Set the Instant Pot to the Saute setting, add 1 tablespoon of olive oil, and once hot add the chicken breasts. Cook for 5-7 minutes on each side, until golden brown. Set aside.
Add 1 tablespoon of olive oil, and once hot again, add onion, mushrooms, and red bell pepper. Cook for about 5-7 minutes, stirring often until they are tender. Add minced garlic, red pepper flakes, chili powder, thyme, oregano, salt, and pepper and cook an additional minute. Add flour and stir to coat vegetables. Add tomato paste and do the same.
Pour white wine into the pot and scrape up any tidbits on the bottom of the pan while stirring the vegetables to help form a paste. Slowly add chicken broth while continuing to stir to break up the paste into a smooth liquid. Add diced tomatoes and stir. Set chicken breasts on top as well as bay leaves.
Place the lid on with the vent closed and set to Meat/Stew setting, on 'more' (or 'high'), and set the timer for 15 minutes. Once it is done cooking, quick release the seal on the lid.
Remove chicken breasts from the pot and discard the bay leaves. Shred the chicken with a fork and add back to the pot, stir, and serve.