I will present a formula relating the second Chern character of a hermitian holomorphic vector bundle on a Kaehler manifold to that of the associated graded sheaf with respect to a filtration by reflexive subsheaves. This generalizes the classical Bott-Chern formula when the subsheaves are holomorphic subbundles, and King's formula for holomorphic sections of bundles. The proof relies on a monotonicity formula and the gauge fixing theorems of Uhlenbeck. If time permits I will discuss an application to the Yang-Mills flow.