Place the grated zucchini in a clean kitchen towel and squeeze out excess moisture. Set aside.
In a large mixing bowl, combine the finely chopped or ground chicken breast, grated zucchini, eggs, oat flour, grated Parmesan cheese, minced garlic, chopped parsley, salt, and black pepper. Mix thoroughly until all ingredients are well incorporated.
Heat 1 tablespoon of olive oil in a large non-stick skillet over medium heat.
Using a 1/4 cup measuring cup, scoop the fritter mixture and gently shape into patties. Place them in the hot skillet, making sure not to overcrowd the pan. You should cook in batches if necessary.
Cook the fritters for about 5-6 minutes on each side, or until they are golden brown and cooked through. The internal temperature of the chicken should reach 165°F (74°C).
Add the remaining 1 tablespoon of olive oil to the skillet before cooking the next batch of fritters.
Once cooked, transfer the fritters to a plate lined with paper towels to drain any excess oil.
Serve warm with your favorite dipping sauce or a side salad.