Nancy: What are you wearing for the costume party?
Marco: I’m going to wear a bear hat, a penguin coat, and cheetah pants. I’ll be the weird one of the party.
Nancy: You’re really going to let your freak flag fly, huh?
Marco: Thanks. You know me; I’m always trying to be fun.
Meaning: "Let your freak flag fly" is a positive expression used to show a characteristic that’s hidden or overt implying a unique or unconventional way of thinking. Some people feel that the work “freak” might be a bad thing, but in this instance, it’s a show of approval.
Barbara: What do you think about my idea for the holiday party we all wear our clothes inside out?
Tom: I’m not sure. That seems a little crazy. Don’t you think?
Barbara: Oh, come on! Let your freak flag fly! Not everything has to be formal in life.
Tom: You know what? You’re right. We should have a little fun in the office every now and again.
Meaning: In this instance, “Let your freak flag fly” is used to show a unique way of thinking, that although may seem strange, can be a positive thing. Here Barbara is just trying to create a fun atmosphere for the day. It doesn’t necessarily mean it’s a permanent condition or thought.