Bring chicken broth to a boil. Cook orzo in the boiling broth, stirring occasionally, until cooked through but firm to the bite, about 8 to 10 minutes. Remove from heat; do not drain.
Heat a large skillet over medium-high heat; cook and stir turkey in the hot skillet until crumbly and evenly browned, about 10 minutes. Stir garlic and red pepper flakes into turkey; cook for 1 minute. Reduce heat to medium. Add spinach, broccoli, tomatoes, peas, carrots, orzo, and broth to the turkey mixture and cook, stirring often, until spinach is wilted and tomatoes begin to split, 5 to 10 minutes. Season with salt and black pepper.
