Seed streamlines on a regular grid

pts = Tuples[Range[-2.5, 2.5, 0.5], 2];

StreamPlot[{Cos[x + y ^ 3], Sin[y + x ^ 3]}, {x, -3, 3}, {y, -3, 3}, StreamPoints -> {pts -> Thick, Automatic, {Forward, Scaled[0.25]}}, Epilog -> {PointSize[0.015], Magenta, Point[pts]}, StreamScale -> None, StreamColorFunction -> "Rainbow"]

-Graphics-