We prove two flat descent results in the setting of Artin n-stacks. First of all, a stack for the etale topology which is an Artin n-stack (in the sense of Simpson and Toën–Vezzosi) is also a stack for the flat (fppf) topology. Moreover, an n-stack, for the fppf topology, which admits a flat (fppf) n-atlas is an Artin n-stack (i.e. possesses a smooth n-atlas). We deduce from these two results a comparison between etale and fppf cohomologies (with coefficients in non-smooth group schemes and also non-abelian). This work is written in the setting of the derived stacks of Toën and Vezzosi, and all of these results are therefore also valid for derived Artin n-stacks.
