Wind turbine wake poses a significant challenge in wind farm operations, affecting power generation efficiency. This study introduces a Dynamic Wake Flow Estimation (DWFE) framework designed to predict wind turbine wake evolution from sparse measurement data. The framework integrates Gaussian Process Regression (GPR), Proper Orthogonal Decomposition (POD), and Long Short-Term Memory (LSTM) networks. Specifically, GPR plays a pivotal role in DWFE by enabling the transformation of flow fields discrete sensor signals into coherent, low-dimensional flow fields which is crucial for accurate flow field predictions, while POD aids in dimensionality reduction and LSTM forecasts temporal wake dynamics, improving both predictive accuracy and computational efficiency. Parametric analysis demonstrates that the robustness and adaptability of the framework improve prediction accuracy with increased sensor density and flexible POD modes. The DWFE framework demonstrates high accuracy in wake flow estimation even with limited data, effectively capturing dynamic wake behavior. Future work will extend this approach to various topographic and climatic conditions, optimizing computational efficiency, and improving interpretability. These advancements will expand the framework's applicability in wind energy and other engineering fields requiring precise flow prediction, emphasizing DWFE's potential in advancing wind farm design, operation and renewable energy optimization.