Walt whitman subscribed to the organic theory of writing (the style must be organically part of the meaning, not imposed mechanically in any way). how does he achieve this in “song of myself”?

Walt Whitman achieved the organic theory of writing in his "Song of Myself" by addressing a variety of topics (fashion, politics and food, among others) in his poem and by approaching all of them from the notion of nature by using metaphors, so as to imply that things happen “organically or naturally” and not mechanically or artificially.  Here is an excerpt to illustrate this idea:  

“This is the grass that grows wherever the land is and the water is,

This the common air that bathes the globe.”

Here Whitman compares the nature with which grass grows where water is with the process of learning. He implies that it's important to learn through experience and not through books or teachers.