In a mixing bowl, combine the softened cream cheese with the diced artichoke hearts, roasted red peppers, olives, and cooked rotisserie chicken. Use a spatula or spoon to mix everything together until well combined.
Lay a flatbread or wrap on a clean cutting board. Spread a generous layer of the cream cheese mixture over the entire surface of the flatbread, leaving about an inch at the edges. Sprinkle a handful of baby spinach on top.
Starting from one edge, carefully roll the flatbread tightly into a log shape. Repeat this process with the remaining flatbreads and filling.
Using a sharp knife, slice each rolled pinwheel into 1-inch pieces. Arrange them on a serving platter and enjoy immediately, or chill in the refrigerator for an hour.
