Vanishing Chern classes for numerically flat Higgs bundles

I consider Higgs bundles satisfying a notion of ampleness that was introduce Bruzzo, Gra~na Otero and Hern'andez Ruip'erez, and prove that the Chern classes of rank $r$ H-ample Higgs bundles over dimension $n$, polarized, smooth, complex, projective varieties are positive under opportune hypothesis. I extend this to non-negativeness of Chern classes of all numerically effective Higgs bundles; and use this condition to prove the vanishing of Chern classes of numerically flat Higgs bundles.