Abstract: 

We develop a flow-based approach to a class of distribution-flow-dependent stochastic differential equations and their particle approximations, motivated by nonlinear Fokker--Planck equations with signed initial data. For a two-point interaction model with globally Lipschitz coefficients, we derive quantitative propagation of chaos bounds in Wasserstein-type distances adapted to signed measures. For convolution-type coefficients under Sobolev regularity assumptions, we prove well-posedness and quantitative approximation estimates for both the flow-dependent equation and the associated particle system. In the additive-noise case, we reformulate the problem in a pathwise ODE form and obtain the corresponding well-posedness and convergence results. We also discuss the two-dimensional vortex model with the Biot--Savart kernel, where a logarithmic modulus of continuity and the Bihari--LaSalle inequality play a central role, and finally obtain the propagation of chaos for the non-degenerate stable-noise case.