Cook potatoes in a large saucepan in boiling water to cover 15 minutes or until tender. Drain and cool. Cut potatoes into 1/8-inch-thick slices; set aside.
Combine cream cheese and next 3 ingredients in a small bowl, mixing well. Set aside. Combine tomato, olives, and vinegar in a small bowl; toss gently. Set aside. Cut 2 circles from each flour tortilla, using a 4-inch round cookie cutter. Spread cheese mixture evenly over tortilla circles. Overlap potato slices around edges of tortillas to form circles. Coat potato slices with cooking spray.
Place a baking sheet in a 400° oven for 5 minutes. Remove from oven; immediately arrange tarts on hot baking sheet, and bake 8 to 10 minutes or until hot and tortillas are crisp. Spoon tomato mixture evenly onto centers of tarts; sprinkle with chives. Serve immediately.