  We provide a method to select flows of solutions to the Cauchy problem for
linear and nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) for
measures on Euclidean space. In the linear case, our method improves similar
results of a previous work of the author. Our consideration of flow selections
for nonlinear equations, including the particularly interesting case of
Nemytskii-type coefficients, seems to be new. We also characterize the
(restricted) well-posedness of FPK equations by the uniqueness of such
(restricted) flows. Moreover, we show that under suitable assumptions in the
linear case such flows are Markovian, i.e. they fulfill the Chapman-Kolmogorov
equations.
