Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners or lightly grease it.
In a large bowl, combine the shredded zucchini and salt. Let it sit for about 10 minutes to draw out excess moisture. After 10 minutes, squeeze the zucchini in a clean kitchen towel to remove as much liquid as possible.
In another bowl, mix together the cooked chicken, cheddar cheese, Parmesan cheese, flour, baking powder, garlic powder, onion powder, and black pepper.
In a separate bowl, whisk together the eggs, milk, and olive oil until well combined.
Add the squeezed zucchini to the chicken and cheese mixture, then pour in the egg mixture. Stir until just combined, being careful not to overmix.
Divide the batter evenly among the muffin cups, filling each about 3/4 full.
Bake for 20-25 minutes, or until the muffins are golden brown and a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.