Place the softened cream cheese into a small mixing bowl.
Whip the cream cheese until it becomes light, smooth, and easy to spread. This creates a creamy base that will blend evenly with the remaining filling ingredients.
Add the feta, dried cranberries, and chopped chives to the whipped cream cheese, keeping the tortillas aside.
Stir thoroughly until the mixture is evenly distributed and forms a cohesive spread with balanced flavor throughout.
Lay out each flour tortilla and coat the surface evenly with the cream cheese mixture, spreading it all the way across for consistent filling in every slice.
Roll each tortilla firmly into a compact log, keeping the filling enclosed as tightly and evenly as possible.
Wrap every rolled tortilla securely in plastic wrap so the shape is preserved and the tortillas do not dry out.
Refrigerate the wrapped rolls for at least 1 hour, allowing them to firm enough for cleaner slicing.
Remove the plastic wrap after chilling, then cut the tortilla rolls into slices of the preferred thickness.
Arrange the sliced pieces on a serving platter and serve chilled.