Combine coconut flour, Italian seasoning, and garlic powder in a medium bowl.
Place chicken breasts in a one-gallon plastic freezer bag and pour seasoned flour mixture on top. Seal bag and turn several times until chicken is evenly coated.
Select “Sauté” function on Instant Pot® and set to high. Add one tablespoon olive oil. Once hot, remove chicken from bag shaking off excess flour mixture. Add enough chicken to cover bottom without overcrowding, working in batches, if necessary.
Brown chicken on each side, approximately 3 minutes per side. Remove and repeat with remaining chicken, adding more olive oil as necessary for each batch. Remove chicken breasts after you've browned them.
Add butter to Instant Pot®. Once melted, add mushrooms and red onion. Cook, stirring frequently, until mushrooms turn brown and the onions soften, approximately 5-6 minutes.
Add Marsala wine and chicken broth and deglaze bottom of the cooking container by gently scraping up the brown bits with a plastic spatula.
Turn Instant Pot® off and add browned chicken to the pot and cover. Lock the lid and set the pressure valve to “Sealing.” Press the “Manual” button and adjust setting to “high.” Set cook time to 10 minutes.
When the cook time is finished, allow pressure to release naturally for 10 minutes, and then do a quick release for any remaining pressure. Turn the unit off and remove lid. Transfer chicken to a serving platter and rest for 5 minutes.
To make the sauce, temper heavy cream with approximately 2 tablespoons of the hot liquid from Instant Pot®. Once tempered, add cream/IP liquid mixture, cream cheese, and chopped parsley to the pot. Season with salt and black pepper, to taste, and stir to combine and make the marsala sauce.
Top each chicken breast with the creamy mushroom sauce and serve immediately.