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This article studies the long-time asymptotic behavior of solutions for the non-autonomous $p$-Laplacian equation $$ u_t-\Delta_pu+ |u|^{p-2}u+f(u)=g(x,t) $$ with dynamic flux boundary conditions $$ u_t+|\nabla u|^{p-2}\frac{\partial u}{\partial\nu}+f(u)=0 $$ in a n-dimensional bounded smooth domain $\Omega$ under some suitable assumptions. We prove the existence of a pullback attractor in $\big(W^{1,p}(\Omega)\cap L^q(\Omega)\big)\times L^q(\Gamma)$ by asymptotic a priori estimate.