Heat olive oil in a pot over medium heat; cook and stir garlic in the hot oil until lightly browned, 1 to 2 minutes. Pour in chicken broth and bring to a simmer. Add tomatoes and spinach; simmer until flavors blend, about 25 minutes. Season with red pepper flakes, salt, and black pepper.
Fill a large pot with lightly salted water and bring to a rolling boil. Once the water is boiling, stir in tortellini and return to a boil. Cook until tortellini float to the top, 3 to 4 minutes; drain.
Mix tortellini into tomato mixture; simmer for 5 more minutes.