Holling's sister considers herself a flower child because she believes in peace and is against violence of any sort. For example, Heather is against the Vietnam War. In the novel, she tells her father that fifty thousand flower children protested the war at the Pentagon.
As a bit of background, the flower power movement of the late 1960s rejected traditional American values and demonstrated new attitudes towards drugs, premarital sex, alternative sexualities, and health. Many historians characterize the flower movement as a sort of hippie rebellion. The flower children reveled in a new era of free love, became enchanted with Eastern philosophy and religions, and explored new alternatives to the traditional American diet. Vegetarianism rose in popularity, as did communes, health foods, and peasant clothing. Many women wore flowers in their hair, symbolizing their support for peace, love, and unity.
In the book, Heather closely identifies with this movement. At one point, she paints a bright yellow flower on her cheek to show her support for the movement, which thoroughly horrifies her father. Mr. Hoodhood is adamant that no daughter of his will be known as a flower child. Undaunted, Heather explains,
A flower child is beautiful and doesn't do anything to harm anyone. . . We believe in peace and understanding and freedom. We believe in sharing and helping each other. We're going to change the world.
More than a little irritated, Mr. Hoodhood asserts that "a flower child. . . is a hippie who lives in Greenwich Village in dirty jeans and beads and who can't change a pair of socks." What Mr. Hoodhood doesn't realize is that Heather's support for the flower power movement is her way of rebelling against his hypocrisy and self-absorption. Heather maintains to Holling that, although her attempt at asserting herself fell flat, she is happy she made the effort to defend her individuality.