Place parsley, garlic, oregano, vinegar, red pepper flakes, salt, and pepper (to taste) in the bowl of a food processor fitted with a blade attachment. Process until finely chopped, stopping and scraping down the sides of the bowl with a rubber spatula as needed, about 1 minute total.
With the motor running, add oil in a steady stream. Scrape down the sides of the bowl and pulse a few times to combine. Transfer sauce to an airtight container and refrigerate at least 2 hours or up to 1 day to allow the flavors to meld. Before serving, stir and season as needed. The chimichurri will keep in the refrigerator for up to 1 week.