In a food processor, combine the crumbled feta cheese and softened cream cheese.
Pulse the mixture until creamy but slightly textured.
Add olive oil, lemon juice, lemon zest, and minced garlic then process for 15 seconds.
Transfer the base mixture to a mixing bowl.
Fold in the chopped green olives, dill, parsley, and red pepper flakes using a spatula.
Season with black pepper to taste.
Refrigerate for 30 minutes to allow flavors to develop before serving.