Two of Whitman's poems especially emphasize his love for America, her democratic form of government, and the freedom American citizens enjoy. They are "One's-Self I Sing" and "I Hear America Singing."

In "One's-Self I Sing," Whitman celebrates the individual, "a simple separate person," but he also celebrates "the word Democratic, the word En-Masse." Thus the poem embraces the value of each person living within a democratic society, the American society. In the poem's last stanza, Whitman "sings" of life filled with "passion, pulse, and power." This life is a cheerful one because it is "freest action formed under the laws divine." The inference is that a democratic government, founded upon the recognition of man's god-given rights, offers the freedom that makes life worth living.

Similar themes are developed in "I Hear America Singing." In Whitman's poem, the country "sings," suggesting happiness and celebration. "Singing" then becomes a metaphor for doing the work one chooses to do and in which one finds happiness. Using the catalog technique, Whitman lists the kinds of ordinary Americans who make a good life for themselves: a carpenter, a mason, a boatman, a shoemaker, a woodcutter, and mechanics. Also included in Whitman's catalog are women, the homemakers--a mother, a young wife, and a girl. The idea of the goodness of American freedom is developed in each person's being able to pursue "what belongs to him or her and to none else." 

Look to his poem "Song of Myself".  There are so many different quotes and ideas in that poem that support freedom and democracy.  In section 10, he describes helping a runaway slave, sitting at the same table as him, letting him dress in his clothes and sleep in his house until he was recovered.  That supports the concept of freedom and democracy for all men; a concept that was highly controversial at that time period.  In section 19, Whitman describes how he sets a meal where everyone is welcome and none are turned away.  In a democracy, people have the freedom to be equal, and for their voices to be heard.

Another great poem to use is from Leaves of Grass, the First Annex:  Sands at Seventy, called "Election Day, 1884" where Whitman describes what he feels to be the most powerful force on earth:  voting.  That is a great poem to use in support of democracy and freedom.  Another one from the same section is "America" where he describes all people in America as being equal and enjoying freedom.

I have provided links to all of these poems-one to "Leaves of Grass" with the latter 2 poems I mentioned, and one to "Song of Myself" with the first 2 poems.  Good luck!

You have most of the examples you will need.  I would just suggest that you take a poem like "Song of Myself" and look at the many lists of things that catalogues.  There is no subjugating of anything to anything else:  slaves, men, women, citizen, immigrants, straights, gays, in all of their many roles ... all of them appear together, each tumbling after the other, all of them part of the great American mix.

To me this is an almost mystical vision of the unity of all things.  Even without using the word "democracy" we get a great sense of the "melting pot" that was the America of his time.

You might want to read "Democratic Vistas" to see more of Whitman's thinking.  By the time he wrote it he was despondent about what was going on in America, but we learn a great deal about him from it.