Dissolve cornstarch in water; add gradually to skillet and cook until thick and bubbly. Remove from heat. Heat 1/8" oil in another skillet over medium heat until hot.
Separate tortillas and saute, one at a time, a few seconds on each side, until limp. (Do not cook too long or they will become crisp and impossible to roll.) Drain on paper toweling.
Fill each tortilla with about 2 heaping tbsp. chicken mixture across center, keeping filling 1" from edges.
Roll tortilla around filling. Place two or three flautas, seam side down, in hot oil.
Saute, turning on all sides, until crisp, about 30 seconds. Drain on paper toweling; keep warm while frying the rest.
Serve with sour cream as a dip.