MeshFunctions -> {"ArcLength"}partly work.
poly = RandomPolygon[10];
plot=ListLinePlot[Append[#, First@#] &@poly[[1]],
MeshFunctions -> {0 &, "ArcLength"}, Mesh -> {Subdivide@10},
MeshStyle -> Red, Epilog -> {Opacity[.2], poly}, Axes -> False]
pts =Cases[plot // Normal, Point[p_] :> p, -1] // DeleteDuplicates
