This work is concerned with the existence and uniqueness of generalized (mild or distributional) solutions to (possibly degenerate) Fokker-Planck equations $ρ_t-Δβ(ρ)+{\rm div}(Db(ρ)ρ)=0$ in $(0,\infty)\times\mathbb{R}^d,$ $ρ(0,x) \equiv ρ_0(x)$. Under suitable assumptions on $β:\mathbb{R}\to\mathbb{R},\,b:\mathbb{R}\to\mathbb{R}$ and $D:\mathbb{R}^d\to\mathbb{R}^d$, $d\ge1$, this equation generates a unique flow $ρ(t)=S(t)ρ_0:[0,\infty)\to L^1(\mathbb{R}^d)$ as a mild solution in the sense of nonlinear semigroup theory. This flow is also unique in the class of $L^\infty((0,T)\times\mathbb{R}^d)\cap L^1((0,T)\times\mathbb{R}^d),$ $\forall T>0$, Schwartz distributional solutions on $(0,\infty)\times\mathbb{R}^d$. Moreover, for $ρ_0\in L^1(\mathbb{R}^d)\cap H^{-1}(\mathbb{R}^d)$, $t\to S(t)ρ_0$ is differentiable from the right on $[0,\infty)$ in $H^{-1}(\mathbb{R}^d)$-norm. As a main application, the weak uniqueness of the corresponding McKean-Vlasov SDEs is proven.