After Bigger commits his crime, he begins to lose his fear of the white society that had, until then, always controlled him and held him down. By murdering a white woman, Bigger feels that he has finally struck back at the white world that he has feared and hated.
The author, Richard Wright, gives us a glimpse into Bigger's thoughts:
The thought of what he had done, the awful horror of it...formed for him for the first time in his fear-ridden life a barrier of protection between him and a world he feared. He had murdered and had created a new life for himself. It was something that was all his own, and its was the first time in his life he had had anything that others could not take from him.
Although he knows that he must escape from punishment, Bigger feels that his destiny is -- for the first time in his life -- in his own hands:
As long as he moved carefully and knew what he was about, he could handle things...As long as he could take his life into his own hands and dispose of it as he pleased, as long as he could decide just when and where he would run to he need not be afraid.
Perhaps this is why the author named the middle section of his book "Flight," rather than "Escape" or "Running Away." Bigger imagines that he is rising and flying above the constraints that white society has always placed on him.
Of course the sad truth is that Bigger will eventually meet his fate; that, of course, is the title of the third section of this novel.