The efficient construction of accurate channel knowledge maps (CKMs) is crucial for unleashing the full potential of environment-aware wireless networks, yet it remains a difficult ill-posed problem due to the sparsity of available location-specific channel knowledge data. Although diffusion-based methods such as denoising diffusion probabilistic models (DDPMs) have been exploited for CKM construction, they rely on iterative stochastic sampling, rendering them too slow for real-time wireless applications. To bridge the gap between high fidelity and efficient CKM construction, this letter introduces a novel framework based on linear transport guided flow matching (LT-GFM). Deviating from the noise-removal paradigm of diffusion models, our approach models the CKM generation process as a deterministic ordinary differential equation (ODE) that follows linear optimal transport paths, thereby drastically reducing the number of required inference steps. We propose a unified architecture that is applicable to not only the conventional channel gain map (CGM) construction, but also the more challenging spatial correlation map (SCM) construction. To achieve physics-informed CKM constructions, we integrate environmental semantics (e.g., building masks) for edge recovery and enforce Hermitian symmetry for property of the SCM. Simulation results verify that LT-GFM achieves superior distributional fidelity with significantly lower Fréchet Inception Distance (FID) and accelerates inference speed by a factor of 25 compared to DDPMs.