Cook 1 cup of the oil, the garlic, oregano, orange zest, and pepper flakes in a small saucepan over low heat until the garlic is softened, about 18 minutes.
Remove the saucepan from the heat and gently stir in the feta and olives. Cover and let sit until the mixture reaches room temperature, about 1 1/2 hours.
Stir in the remaining 1/4 cup oil and serve. (The mixture can be transferred to an airtight container and refrigerated for up to 1 week. Before serving, let sit at room temperature until the oil liquefies about 1 hour.).