Preheat oven to 425F and line a baking sheet with foil, grease with oil or cooking spray
Shred Zucchini using the large holes of a box grater, squeeze dry in a clean kitchen towel (should have 2 cups.)
Heat oil in a large skillet over medium-high heat. Add zucchini, ground chicken, chili powder, onions, cumin and salt. to pan and cook, stirring until the chicken is cooked through 8-10 minutes.
Spread tortillas out on a baking sheet in two overlapping rows. Bake until hot, about 2 minutes, transfer to a plate and cover.
Line the baking sheet with foil or parchment paper (for easier clean up) and coat with cooking spray. Place 6 tortillas on a clean cutting board or extra pan. Working quickly, spread a generous ¼ cup chicken mixture along the bottom third of a tortilla, sprinkle with about 1T cheese and tightly roll into a cigar shape.
Generously coat the top and sides of taquitos with cooking spray. Sprinkle the top with salt, liberally. Bake the taquitos until browned and crispy, 14 to 18 minutes.