Mule ESB allows users to create a file input and output flow using the file and logger components. The flow involves creating a Mule project in Anypoint Studio, dragging a file input component, Java component, and file output component into the message flow, configuring the input and output file paths, and adding a logger to print messages to the console. Running the flow will transfer a file from the input to backup folder and then to the output folder, logging the file name in the process.