Best tool to plot "streamlines"?

Question

I wanna plot a velocity profile, this is what I have: (https://i.sstatic.net/Z319A.png)

but I want something like this: (https://i.sstatic.net/yGeP6.png)

Data set is X and Y coordinates (basically a grid, e.g. 256x256, containing every coordinate) 3rd column is velocity.

So far I only found out it's not achievable in Gnuplot so I suppose my next best option would be Python. What would be the easiest way for this in python? I'm not even sure if what I need is indeed streamline plotting, I just want to achieve what is in the second photo attached.