Successive-cancellation list (SCL) decoding of polar codes has been adopted for 5G. However, the performance is not very satisfactory with moderate code length. Heuristic or deep-learning-aided (DL-aided) flip algorithms have been developed to tackle this problem. The key for successful flip decoding is to accurately identify error bit positions. In this work, we propose a new flip algorithm with help of differentiable neural computer (DNC). New state and action encoding are developed for better DNC training and inference efficiency. The proposed method consists of two phases: i) a flip DNC (F-DNC) is exploited to rank most likely flip positions for multi-bit flipping; ii) if decoding still fails, a flip-validate DNC (FV-DNC) is used to re-select error bit positions for successive flip decoding trials. Supervised training methods are designed accordingly for the two DNCs. Simulation results show that proposed DNC-aided SCL-Flip (DNC-SCLF) decoding demonstrates up to 0.34dB coding gain improvement or 54.2 reduction in average number of decoding attempts compared to prior works.