I think you can argue that Equality 7-2521 definitely achieves freedom. His escape from the World Society is only the beginning of his freedom. Mostly, his freedom lies in his ability and desire to fend for himself and the Golden One and to live, as he likes, at the opposite edge of the Uncharted Forest.
Equality 7-2521's freedom is best illustrated at the end of the story. First, he changes his name, freeing him from the society's last grip on his identity. He also figures out that he can use the word "I," to describe himself and talk about himself. I think the best passage from the text that illustrates Equality 7-2521's, er, I mean Prometheus's, new found freedom is this:
I shall live here, in my own house. I shall take my food from the earth by the toil of my own hands. I shall learn many secrets from my books. Through the years ahead, I shall rebuild the achievements of the past, and open the way to carry them further, the achievements which are open to me, but closed forever to my brothers, for their minds are shackled to the weakest and dullest ones among them.
As you can see, this passage illustrates Prometheus's freedom through his desire for discovery and also through the shackles that hold his brothers captive back in the World Society.