Heat olive oil and butter in a large deep skillet or Dutch oven over medium-high heat until butter is melted and foamy.
Season chicken breasts evenly with salt and black pepper on both sides.
Add chicken breasts to the skillet and cook for 5-6 minutes on each side until golden brown and cooked through. Remove chicken from skillet and set aside on a plate.
Add sliced mushrooms to the same skillet and sauté for 5 minutes until they release their moisture and start to brown.
Add chopped onion and minced garlic to the mushrooms and cook for 2-3 minutes until the onion is translucent and garlic is fragrant.
Pour in the white wine and cook for 2 minutes, scraping the bottom of the skillet to deglaze and reduce the wine slightly.
Add chicken broth, heavy cream, grated Parmesan cheese, dried thyme, and crushed red pepper flakes. Stir well to combine and bring the mixture to a gentle simmer.
Add fresh baby spinach leaves to the sauce and cook for 2-3 minutes until the spinach wilts.
Return the cooked chicken breasts to the skillet, spoon some sauce over them, and simmer for an additional 3-4 minutes to heat through and meld flavors.
Taste the sauce and adjust seasoning with additional salt and pepper if needed.
Serve the creamy chicken mushroom Florentine hot, spooning extra sauce over the chicken.