Conserved gravitational charges are commonly expressed as surface integrals of the metric perturbation and its first derivatives. We show that, in the usual asymptotically AdS and asymptotically flat settings, the standard charges admit equivalent representatives as fluxes of linearized curvature. The construction uses a divergence-free rank-four tensor whose trace is proportional to the cosmological Einstein tensor. On a maximally symmetric AdS background, it reproduces the known curvature representation of the Abbott-Deser charges. The asymptotically flat construction is not obtained by taking the naive $\Lambda \to 0$ limit, since the Killing two-form vanishes for translations. We instead introduce an antisymmetric Poincaré Killing potential. A representative Killing potential adapted to the algebraic Bianchi identity converts the linearized Einstein current into a total divergence and yields a single curvature-flux formula. Its translation sector reproduces the ADM energy–momentum, while its Lorentz sector reproduces the angular momentum and boost/center-of-mass charges under the standard Regge–Teitelboim falloff and parity conditions, in any dimension $n>3$. The normalization is checked explicitly for Schwarzschild, boosted Schwarzschild, Kerr, Schwarzschild–Tangherlini, and Myers–Perry data. On non-maximally symmetric Einstein backgrounds, background Weyl curvature generates additional terms, so the maximally symmetric construction does not directly extend to a pure codimension-two curvature-flux formula; for perturbations of Schwarzschild–AdS and slowly rotating Kerr–AdS backgrounds, we show explicitly that these terms have vanishing flux at infinity.