Deep learning-based image enhancement methods face a fundamental trade-off between computational efficiency and representational capacity. For example, although a conventional three-dimensional Look-Up Table (3D LUT) can process a degraded image in real time, it lacks representational flexibility and depends solely on a fixed prior. To address this problem, we introduce FlowLUT, a novel end-to-end model that integrates the efficiency of LUTs, multiple priors, and the parameter-independent characteristic of flow-matched reconstructed images. Specifically, firstly, the input image is transformed in color space by a collection of differentiable 3D LUTs (containing a large number of 3D LUTs with different priors). Subsequently, a lightweight content-aware dynamically predicts fusion weights, enabling scene-adaptive color correction with $\mathcal{O}(1)$ complexity. Next, a lightweight fusion prediction network runs on multiple 3D LUTs, with $\mathcal{O}(1)$ complexity for scene-adaptive color correction.Furthermore, to address the inherent representation limitations of LUTs, we design an innovative iterative flow matching method to restore local structural details and eliminate artifacts. Finally, the entire model is jointly optimized under a composite loss function enforcing perceptual and structural fidelity. Extensive experimental results demonstrate the effectiveness of our method on three benchmarks.