I love Walt Whitman, and this particular section is very interesting. It is almost like several poems merged as one; in the first half, he discusses hunting, sailing, clamming, and sitting with a trapper that had married an indian woman, and sharing a meal. The second half describes the relief and aid that he gave to a runaway slave, and how it was disconcerting for the slave, since he wasn't used to kind treatment from white men. In both, there is a theme of all men-white men, indian men, and black men-being completely and totally equal, and worth equal treatment. It was a controversial stance to take at the time, as abolitionism and the civil rights issues were in the spotlight.
For symbolism, Whitman tends to be quite straightforward in his descriptions; his language isn't as layered with symbolism as many other poets can be. But, if you look at the way he describes something, it can be a symbol of his feelings towards it. For example, he describes his hunting trip as being filled with "lightness and glee," symbolizing his felicity as he hunts; the trapper "lounged", had a "luxuriant beard", and his bride had "voluptuous limbs,"-all of these descriptions symbolizing the complete ease, health, vivacity and happiness this couple finds in what others of the time might have considered an "inappropriate" bi-racial relationship. Later, as Whitman has the slave "sit next me at table" and "gave him a room that enter'd from my own," Whitman is symbolizing how he feels the slave is equal to him. His room is connnectd, or joined with his; he sits at the same table. Whitman is expressing his views on slavery and equality through those symbols.
I hope that those thoughts get you started; good luck!