Galactic rotation curves are traditionally interpreted as evidence for non-luminous dark matter. This work presents an alternative, information-theoretic mechanism based on the Kilgore Field Equation (KFE), in which physical systems are constrained by information continuity in addition to standard gravitational dynamics. Within the KFE framework, galactic behavior naturally separates into two regimes: (i) a local, conservative coherence mechanism that suppresses structural instabilities through Fisher-information regularization, and (ii) a global, non-conservative entropic force emerging at galactic scales. The latter couples directly to gradients in the coarse-grained information content of the baryonic mass distribution and produces an effective acceleration scaling as 1/r, yielding asymptotically flat rotation curves without invoking particle dark matter. Numerical illustrations demonstrate that for realistic baryonic density profiles, the cumulative configuration entropy grows logarithmically with radius in the halo region, leading naturally to the required long-range behavior. The resulting galactic dynamics align with observed rotation curves while remaining consistent with prior applications of the KFE to black-hole information preservation and chaos regulation in few-body gravitational systems. We emphasize that this work does not propose a replacement for the ΛCDM paradigm at cosmological scales. Rather, it identifies a viable information-continuity mechanism operating at galactic scales, suggesting that flat rotation curves may emerge from coherence enforcement within baryonic matter itself. Together with earlier results, these findings support the existence of a universal information-continuity constraint acting across gravitational regimes.