Add the parsley, oregano, garlic, red wine vinegar, salt, black pepper, and red pepper flakes to a food processor. Pulse a few times to chop the herbs. With the motor running, slowly drizzle in the olive oil until the chimichurri is combined but still slightly chunky. Set aside.

Heat a grill or grill pan over medium-high heat. Toss the zucchini, bell pepper, and onion with the olive oil, salt, and pepper. Grill for 3 to 4 minutes per side until tender and lightly charred.

Move an oven rack to the lower third of the oven, then preheat to 425°F.

Place the flatbreads on a baking sheet. Spread about 3 tablespoons of chimichurri over each flatbread. Arrange the grilled vegetables evenly over the top and sprinkle with the vegan feta.

Bake for 7 to 9 minutes or until the edges are crisp and the flatbread is heated through.

Remove from the oven and top with the arugula. Drizzle with additional chimichurri before slicing and serving.