Preheat oven to 400°F. Season chicken cutlets with salt and pepper, dredge in flour, shaking off excess.
Heat butter and 1 tbsp olive oil in a skillet over medium-high heat. Add chicken and cook until golden-brown, about 3 minutes per side. Remove and cover with foil to keep warm.
Reduce heat to medium, add remaining 1 tbsp olive oil to the skillet. Cook garlic and thyme until fragrant, about 30 seconds. Add spinach and cook until wilted, about 2 minutes.
Stir in chicken broth and cream cheese. Simmer until the cream cheese is melted, then add artichokes and lemon juice. Cook until heated through.
Add the chicken back to the skillet along with any juices. Bring to a simmer, then transfer to the oven for 5–6 minutes, until chicken is cooked through.
Sprinkle with Parmesan and red pepper flakes before serving.