You simply can't. citing the documentation, streamplot
operates in a way that:
"Each cell in the grid can have, at most, one traversing streamline" (link)
Usually playing with the parameter density
helps anyway.
You could always 'manually' integrate each streamline starting from your equispaced points of interest.
In case the data above has an exact left-rigth symmetry (Can't be sure by just looking at the pic) you may get a better result with the solution I gave here: here.