Fixed-length fingerprint representations, which map each fingerprint to a compact and fixed-size feature vector, are computationally efficient and well-suited for large-scale matching. However, designing a robust representation that effectively handles diverse fingerprint modalities, pose variations, and noise interference remains a significant challenge. In this work, we propose a fixed-length dense descriptor of fingerprints, and introduce FLARE-a fingerprint matching framework that integrates the Fixed-Length dense descriptor with pose-based Alignment and Robust Enhancement. This fixed-length representation employs a three-dimensional dense descriptor to effectively capture spatial relationships among fingerprint ridge structures, enabling robust and locally discriminative representations. To ensure consistency within this dense feature space, FLARE incorporates pose-based alignment using complementary estimation methods, along with dual enhancement strategies that refine ridge clarity while preserving the original fingerprint modality. The proposed dense descriptor supports fixed-length representation while maintaining spatial correspondence, enabling fast and accurate similarity computation. Extensive experiments demonstrate that FLARE achieves superior performance across rolled, plain, latent, and contactless fingerprints, significantly outperforming existing methods in cross-modality and low-quality scenarios. Further analysis validates the effectiveness of the dense descriptor design, as well as the impact of alignment and enhancement modules on the accuracy of dense descriptor matching. Experimental results highlight the effectiveness and generalizability of FLARE as a unified and scalable solution for robust fingerprint representation and matching. The implementation and code will be publicly available at https://github.com/Yu-Yy/FLARE.