This work presents a fast successive-cancellation list flip (Fast-SCLF) decoding algorithm for polar codes that addresses the high latency issue associated with the successive-cancellation list flip (SCLF) decoding algorithm. We first propose a bit-flipping strategy tailored to the state-of-the-art fast successive-cancellation list (FSCL) decoding that avoids tree-traversal in the binary tree representation of SCLF, thus reducing the latency of the decoding process. We then derive a parameterized path selection error model to accurately estimate the bit index at which the correct decoding path is eliminated from the initial FSCL decoding. The trainable parameter is optimized online based on an efficient supervised learning framework. Simulation results show that for a polar code of length 512 with 256 information bits, with similar error-correction performance and memory consumption, the proposed Fast-SCLF decoder reduces up to $73.4\%$ of the average decoding latency of the SCLF decoder with the same list size at the frame error rate of $10^{-4}$, while incurring a maximum computational complexity overhead of $27.6\%$. For the same polar code of length 512 with 256 information bits and at practical signal-to-noise ratios, the proposed decoder with list size 4 reduces $89.3\%$ and $43.7\%$ of the average complexity and decoding latency of the FSCL decoder with list size 32 (FSCL-32), respectively, while also reducing $83.2\%$ of the memory consumption of FSCL-32. The significant improvements of the proposed decoder come at the cost of $0.07$ dB error-correction performance degradation compared with FSCL-32.