In a mixing bowl, combine the softened cream cheese, drained diced artichoke hearts, diced roasted red pepper, diced olives, and diced cooked chicken.
Use a hand mixer or stand mixer with the paddle attachment on low speed, or mix by hand with a spatula, until the ingredients are well combined and smooth.
Lay one flatbread or wrap on a work surface and spread about one quarter of the chicken mixture into an even thin layer, leaving a small border at the edge.
Top the spread with a layer of baby spinach leaves.
Roll the flatbread or wrap tightly from one end to the other to form a log.
Trim the ends if desired, then cut the roll into 6 to 8 pinwheels. Repeat with the remaining flatbreads and filling.
For a gluten-free or low-carb option, spoon the chicken mixture into large lettuce leaves and roll or fold to make lettuce wraps instead of using flatbreads.
