Preheat the oven to 400 degrees F.
In a large bowl fold together the goat cheese, cream cheese, garlic and herbs. Season with a pinch of salt and pepper.
Line a sheet tray with parchment paper and lightly flour a work surface. With a rolling pin, roll the dough into an oval shape that fits a half sheet tray and lay out on the parchment paper.
Spread dough with the goat cheese mixture, leaving a 1/2-inch edge. Arrange the red onion in a row, overlapping slightly. Repeat with the zucchini.
Brush the red onion, zucchini, and crust with olive oil. Sprinkle with red pepper flakes, salt and pepper, to taste, and the Parmesan. Bake in the oven for 25 minutes.
Remove from oven and using a pizza cutter, slice into thin strips for serving.