The single-flow zinc–nickel battery (ZNB) is a new type of flow battery with a simple structure, large-scale energy storage, and low cost, and thus has attracted much attention in the battery field recently. The state of charge (SOC) and state of health (SOH) are key indicators of the battery, and their inaccurate estimation can damage the battery. However, little has been done so far to study how to jointly estimate SOC and SOH for the ZNB. In this paper, the method of adaptive IDUKF is proposed. A second-order equivalent circuit model is applied to improve the accuracy. At the same time, the double unscented Kalman filter (DUKF), which is optimized by the improved Harris hawk optimization (IHHO) algorithm, is used to estimate the SOC and parameters online. Then, the capacity update model is introduced to simulate the change in SOH. Finally, the proposed method is applied to a 16 Ah ZNB, and the experimental results confirm the validity of the proposed method.