Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Season the chicken pieces with salt and black pepper.
Add the chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove chicken from skillet and set aside.
In the same skillet, add the sliced mushrooms and cook for 4-5 minutes until they release their moisture and start to brown.
Add the chopped onion and minced garlic to the mushrooms and sauté for 2-3 minutes until the onion is translucent and fragrant.
Pour in the white wine and cook for 2 minutes, scraping the bottom of the skillet to deglaze and reduce the liquid slightly.
Add the chicken broth, heavy cream, dried thyme, and crushed red pepper flakes to the skillet. Stir to combine and bring to a gentle simmer.
Return the cooked chicken to the skillet and cook for 3-4 minutes until the sauce thickens slightly.
Add the fresh baby spinach and cook for 1-2 minutes until wilted.
Stir in the grated Parmesan cheese until melted and the sauce is creamy.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve immediately, spooning the creamy chicken mushroom Florentine over rice, pasta, or crusty bread if desired.