This line, which he expresses in section 6 of his poem "Song of Myself," expresses the sentiment that the grass under his feet is just another emblem that indicates that he is connected with the entire human race. One of the main points of section 6 is to express the thought that when people die and are buried, eventually their bodies become fertilizer feeding the soil. The grass then feeds on those nutrients, growing strong and green essentially off of the remains of people's lives. He expresses this thought when he identifies grass as "the beautiful uncut hair of graves," and as sprouting "from the breasts of young men."
So, when Whitman claims that the grass is the "flag of his disposition," he is literally meaning that it is a representation or symbol of how he feels. "Disposition" means his attitude, beliefs or feelings on an issue, and a flag would be an outward symbol of those feelings. And Whitman feels that life is one continuous ciricle; death does not conquer, it just feeds the circle of life. Grass symbolizes Whitman's belief that all men and women are connected; even though dead, the people buried in the ground sprout as grass, which he then sits and walks on. Thus, he is connected to entire generations of Americans who have passed before him. The grass being a "flag of my disposition" indicates that it represents his belief in the circle of life, his connectedness to everyone else, and the beauty and miracle of life and death. I hope that those thoughts helped; good luck!