The main workflow that you gave is right and one of the names this process is known is optical flow. Matlab has some functions that make most of those steps at once (you can check it here:https://de.mathworks.com/help/vision/ref/opticalflowhs.estimateflow.html).
In case you don't have the image processing you could do a manually implementation of the method. Someone did a good tutorial in matlab that can be found here: https://de.mathworks.com/matlabcentral/fileexchange/48744-lucas-kanade-tutorial-example-1 .
The main additional thing you will need to do is to average only velocities above a given threshold so your result is not distorted by the points with no bubbles.
For the flux rate you can define an area around your division line and calculate the rate with the speeds in this area.
If you want the most exact result possible you will need to track each ball and average the speeds only in the tracked areas. This can be done by find blobs (how your bubles would be called) with image segmentation techniques, you can check this nice tutorial as a reference https://de.mathworks.com/matlabcentral/fileexchange/25157-image-segmentation-tutorial?s_tid=srchtitle .
