In this paper, we establish a propagation of chaos result for mean-field mean reflected backward stochastic differential equations (BSDEs), where both the generator and constraint depend on the distribution of the solution. When the generator does not rely on $z$, under mild Lipschitz and integrability conditions, we prove existence and uniqueness of the solution to the interacting particle system for general reflections. We are able to consider the case where the generator depends on $z$ when the reflection is linear. In both cases, we obtain the convergence rate of solution to the interacting particle system towards the solution to the mean-field mean reflected BSDEs.