Toss chicken with salt, pepper and flour. Shake off excess.
Set Instant Pot to Sauté; add olive oil and brown chicken in batches, 2–3 minutes per side. Remove and set aside.
Sauté onion and mushrooms until softened, about 4 minutes; add garlic and cook 30 seconds.
Pour in Marsala to deglaze, scraping browned bits; add chicken broth, thyme, and return chicken.
Seal and cook on Manual/High for 6 minutes; quick release after 5 minutes rest.
Stir in butter and parsley; taste and adjust seasoning. Serve over mashed potatoes or egg noodles.