Whitman's observation that the grass may be "the flag of my disposition" is given in response to a child asking him what grass is. He freely observes that he does "not know what it is any more than he," but he notes that it is "out of hopeful green stuff woven." We may infer from this, then, that in being the "flag" of Whitman's "disposition," it is behaving as all flags do: as a symbol and a public representation of something. So, if the "flag" is woven out of "hopeful green stuff," we can understand Whitman to be describing his own disposition—that is, his character, nature, and outlook—as being hopeful, optimistic, and green in the sense of forever rejuvenating itself.
Grass, Whitman later says, is found "sprouting alike in broad zones and narrow zones / Growing among black folks as among white." It represents the "uncut hair of graves" and transpires "from the breasts of young men." Grass, then, represents a certain universal quality, a connection that unites all of humanity. It represents the continual growth and death and rebirth of human kind: "the smallest sprout shows there is really no death." If grass in its disposition is similar to Whitman, then, we may assume that he too feels a similar sense of indefatigable optimism, universality, and the desire to survive among all things.