Remaining useful life (RUL) prediction is essential for the prognostic health management (PHM) of industrial equipment, such as aero engines, enabling predictive maintenance and reducing failure risks. Data-driven models have gained significant attention in RUL prediction due to their ability to capture complex nonlinear relationships. However, the variability in data distributions across multiple operating conditions makes it challenging for traditional models to capture temporal and spatial features of equipment operation, leading to unstable prediction performance. To address this issue, this paper proposes a novel LSTM-KAN-DANN transfer learning method for RUL prediction. First, we train a LSTM-Kolmogorov-Arnold Network (KAN) model using multiple source domain datasets, allowing it to extract nonlinear features and provides preliminary RUL estimates. Then, Domain-Adversarial Neural Networks (DANN) is integrated with LSTM-KAN by introducing a domain discriminator and gradient reversal layer. This enables the model to learn domain-invariant features, reducing discrepancies between the source and target domains and improving generalization across different operating conditions. A comparison study using the CMAPSS dataset demonstrates that LSTM-KAN effectively captures nonlinear features, particularly under complicated operating conditions, outperforming traditional methods in generalization. The DANN integration further enhances predictive accuracy in cross-domain scenarios, leading to notable reductions in RMSE and Score across most transfer tasks. The proposed LSTM-KAN-DANN transfer learning framework provides a robust and efficient solution for industrial equipment PHM, offering significant potential for real-world applications.