The ol.style.FlowLine is a line style to draw LineString with variable colors and widths.
This can be used to display flows maps
or Sankey diagram on a map.
NB: the FlowLine style doesn't impress the hit-detection. If you want your lines to be sectionable you have to add a style (with transparent line: stroke color opacity to .1 or zero width) to handle this (see defaultStyle in example or this issue).
Look at this example to see how to set a width and color function to control the line drawing.
It can be used to display elevation as color on a GPX tracks.