We are interested in studying the well-posedness is a non-local singular non-linear Fokker-Planck partial differential equation (PDE) and its associated non-local singular McKean SDE, whose drift coefficient is a function of time taking values in a Besov Space of negative index and its diffusion is unitary. Due to the singularity of the coefficient, we must rely on a notion of solution for singular SDEs that is framed through the rough martingale problem. The solution to a rough martingale problem is a probability measure which corresponds to the law of X, solution to such an SDE. Existence and uniqueness of such a measure relies on the well-posedness of an associated non-local singular non-linear Fokker-Planck PDE, for which existence and uniqueness are proven using a novel linearized strategy. We prove that the solution to the non-local singular McKean SDE is the probabilistic representation of the above mentioned Fokker-Planck PDE. As byproduct of that probabilistic representation, we establish mass conservation and positivity preserving for the PDE.