We present a general framework for distributed wireless information flow allocation problem in multiple access networks, where the end users (EUs) can seek wireless flows from multiple access points (APs). We aim to minimize the power consumption while satisfying each EU's minimum data rate requirement but not violating peak power constraint of each AP and interference constraint monitored by regulatory agents. Toward this end, we model the flow allocation problem as a game which is proved to be a best-response potential game. Then based on potential game theory, we show the existence and uniqueness of Nash equilibrium in the formulated game. Moreover, we demonstrate that the Nash equilibrium is actually the globally optimal solution to our problem. Besides, we propose two distributed algorithms along with convergence analysis for the network to obtain the Nash equilibrium. Meanwhile, we reveal the interesting layered structure of the problem in question. Extensive numerical results are conducted to demonstrate the benefits obtained by flow allocation, as well as the effectiveness of our proposed algorithms.