Melt butter in a skillet over medium heat; stir in flour until smooth. Add onion; cook and stir until onion is softened, 5 to 10 minutes. Add black olives, lemon juice, 1 tablespoon oil, paprika, black pepper, and salt; cook and stir until heated through, about 2 minutes.

Stir in chicken; remove the skillet from heat and cover.

Heat oil in a large, heavy saucepan or deep fryer over medium-high heat.

Fill tortillas with chicken mixture. Roll tortilla around filling and secure with a toothpick.

Working in batches, fry rolled tortillas in hot oil until browned, about 2 minutes. Use a slotted spoon or tongs to transfer tortillas to a paper towel-lined plate; serve warm.