Flat metrics on a surface are a subset of Euclidean cone metrics that is induced by quadratic differentials. There is a natural stratification by prescribing cone angles at singularities. I will describe a simple method to reconstruct the metric locally using the lengths of a finite set of closed curves, which I refer to as a local length rigidity problem. However, the global case has the result that a finite set of simple closed curves cannot be length rigid when the stratum has enough complexity. This is extending a result of Duchin-Leininger-Rafi.