Preheat oven to 400. Mix prepared chicken, 1/2 cup salsa, and cheese in a medium bowl.
Warm 8 tortillas in microwave, 30 seconds on high. Remove and cover with a clean kitchen towel to keep warm.
OPTION: Instead of warming in the microwave and then brushing with oil before baking, you can brush with oil first and then warm in a skillet or griddle. This will begin the crisping process and you won't need to brush with oil again before baking. This can take a little longer because you can usually only do a few at a time in a skillet, but they only need about 30-45 seconds on each side to begin browning slightly. You don't want to crisp them in the skillet, you just want them to start to brown slightly. Then you can remove them to a plate and continue as directed but don't brush again with oil.
Working with 1 tortilla at a time, add roughly 2 tablespoons chicken mixture to the center of tortilla. Roll up. Place seam side down on parchment-lined baking sheet. Repeat with remaining warmed tortillas.
Warm remaining 8 tortillas 30 seconds on high in microwave. Continue filling as directed.
Brush tops and sides of rolled tortillas with oil (if they haven't been brushed already per the optional warming method above). Bake at 400 until browned and crispy, about 15 minutes. Serve with remaining salsa for dipping.