Turn the Instant Pot to the Saute setting on High. Season the chicken with salt and pepper. When the oil is hot, add the chicken skin side down and sear for about 4 minutes, until the skin is golden brown. Flip the chicken with tongs and sear the bottoms until they are also golden brown, another 4 minutes or so. Transfer the chicken to a plate (do this in batches if necessary).
Add the onions to the remaining oil in the pan, and saute until they are golden, about 5 minutes. Add the peppers, mushrooms and garlic and saute for 4 minutes until peppers start to soften. The Saute setting of the Instant Pot will only stay on for 30 minutes, so if you happen to be taking your time with all of this you may have to reset the appliance to the Saute setting.
Add the red wine and stir to loosen up any browned bits that have stuck to the bottom of the Instant Pot. Stir in the crushed tomatoes, tomato paste, oregano and red pepper flakes. Turn off the Saute setting. Add the chicken back to the pot.
Close the lid and set the vent knob to sealed. Set the Instant Pot on High Pressure, for 20 minutes. Once the cooking time has finished, allow the pressure to release naturally for 10 minutes, then open the valve to release any remaining pressure. An internal thermometer inserted into the meaty part of the thigh should read 160°F (the temperature will climb another 5 degrees to a safe internal temperature of 165°F while it is resting).
Serve the chicken in a shallow serving bowl with the vegetables and sauce, sprinkled with the parsley, with the starch of choice if desired.