In this paper, we investigate the flexible power transfer among electric vehicles (EVs) from a cooperation perspective in an energy Internet based EV system. First, we introduce the concept of cooperative EV-to-EV (V2V) charging, which enables active cooperation via charging/discharging operations between EVs as energy consumers and EVs as energy providers. Then, based on the cooperative V2V charging concept, we propose a flexible energy management protocol, which can help the EVs achieve more flexible and smarter charging/discharging behaviors. In the proposed energy management protocol, we define the utilities of the EVs based on the cost and profit through cooperative V2V charging and employ the bipartite graph to model the charging/discharging cooperation between EVs as energy consumers and EVs as energy providers. Based on the constructed bipartite graph, we propose a max- weight V2V matching algorithm, which can lead to an optimized V2V matching in terms of the network social welfare. Simulation results verify the efficiency of our proposed cooperative V2V charging based energy management protocol in improving the EV utilities and the network social welfare as well as reducing the energy consumption of the EVs.