Heat oven to 425°F; parchment-line rimmed metal sheet. Mix chicken, cream cheese, pepper Jack, corn, scallions, cumin, paprika, and salt into thick filling.
Warm tortillas in dry skillet about 15 seconds per side until flexible. Briefly keep under clean towel while working.
Divide filling among tortillas; roll tightly. Arrange seam-side down; lightly brush with oil.
Bake 18 to 22 minutes until crisp and filling 165°F. Carefully turn after 12 minutes if bottoms brown faster.
Refrigerate baked taquitos in shallow container within 2 hours; chill fully. Freeze in one layer until firm; bag, label, and freeze up to 2 months.
Reheat frozen on metal sheet at 400°F for 15 to 20 minutes, turning once, until crisp and center 165°F.
Serve 2 per portion with 2 tablespoons tomato salsa.