Over the past decades, the unmanned aerial vehicle (UAV) has received unprecedented surge of scientific and military interest worldwide. This paper investigates the problem of opportunistic spectrum access for multi-UAV networks from a game-theoretic perspective. Due to the topology of the multi-UAV networks, the interference may be classified into two parts, i.e., the intra-cluster and the inter-cluster interference. Moreover, since the UAVs in the network have different tasks, the communication demand of each UAV should be taken into account. First, we formulate the demand-aware joint channel-slot selection problem as a weighted interference mitigation game, and then, design the utility function considering features of multi-UAV network, e.g., some rewards due to the channel and slots selection. We prove that the formulated game is an exact potential game with at least one pure-strategy Nash equilibrium. Next, we apply the distributed log-linear algorithm to achieve the desired optimization and overcome the constraint of dynamic communication demand of each UAV. To speed up the convergence, we also propose a low-complexity and realistic channel and slot initialization scheme for UAVs. Finally, the simulation results validate the effectiveness of the formulated game.