Season chicken with salt, black pepper, and red pepper flakes.
Heat olive oil in a large deep skillet over medium-high. Sear chicken until golden, 4–5 minutes. Transfer to a plate.
Lower heat to medium. Melt butter in the same pan. Stir in garlic and cook until fragrant, about 30 seconds.
Add orzo and toast, stirring, until lightly nutty, 1–2 minutes.
Pour in white wine to deglaze. Scrape up browned bits and simmer until mostly reduced, 1–2 minutes.
Stir in chicken broth. Bring to a gentle simmer and cook, stirring occasionally, until orzo is just tender, 8–10 minutes.
Return chicken and any juices to the pan. Add heavy cream and Dijon. Simmer until slightly thickened and chicken is cooked through, 3–4 minutes.
Fold in lemon zest, lemon juice, and Parmesan. Stir until smooth and creamy.
Add spinach and wilt gently, 1 minute. Taste and adjust salt or lemon to preference.
Finish with parsley. Let rest 2 minutes to thicken, then serve warm.