Peyton Farquhar begins the story looking down at the flowing creek below him, imagining how he might escape from the Union soldiers that are planning to execute him. His fantasy of escape depends on the current of the stream, which pulls him to safety and tosses him ashore. In this sense, water literally provides our protagonist with freedom.
Even before it saves his life, water is associated with freedom. Having followed the "dancing driftwood" (1.4) with his eyes, Farquhar, in the moments before his death, becomes as free as the floating branch. As the ending of the story proves, however, Farquhar's body is never free and he never escapes military justice. Though his mind flows freely (perhaps a normal reaction to imminent death), his body stays in one place. By making a flowing current central to his story, Bierce makes his protagonist's wandering mind – his freewheeling imagination – fit right in.