We investigate the lifetime of magnetically trapped atoms above a planar, layered atom chip structure. Numerical calculations of the thermal magnetic noise spectrum are performed, based on the exact magnetic Green function and multilayer reflection coefficients. We have performed lifetime measurements where the center of a side guide trap is laterally shifted with respect to the current carrying wire using additional bias fields. Comparing the experiment to theory, we find a good agreement and demonstrate that for a chip whose topmost layer is metallic, the magnetic noise depends essentially on the thickness of that layer, as long as the layers below have a much smaller conductivity; essentially the same magnetic noise would be obtained with a metallic membrane suspended in vacuum. Based on our theory we give general scaling laws of how to reduce the effect of surface magnetic noise on the trapped atoms.