<p>Most people, articles, videos, etc. refer to printing speed by linear speed (mm/s), but a lot of YouTubers prefer to talk about volumetric flow (mm<sup>3</sup>/s) (mm cubed per second).  I suspect that at some point in the past year or three, some of the more engineer-y types switched to this new measurement standard, but I'm not entirely sure what happened.  What is the practical difference between using linear speed vs flow rate to determine print speed?</p>
<p>For a follow-up, how can you go about changing your print speed as a flow rate in a slicer?  It's easy to find the linear speed, but I have not found the flow rate speed.  I use Cura and will start using Prusa Slic3r soon.</p>

Flow rate adds a dimension to the regularly used printing speed. Note that maximum volumetric flow is determined by the hotend (unless your extruder is under dimensioned or highly geared) as it cannot supply more molten filament than it can melt in a certain time.
So, instead of specifying the print speed, you should include the amount of material it can process. Volumetric flow includes nozzle diameter, layer thickness and hotend type.
E.g. a 60 mm/s of a 0.4 mm nozzle at a 0.2 mm  layer height has a very different volumetric flow (4.8 mm³/s) from a 60 mm/s 0.8 mm nozzle at a 0.4 mm  layer height (19.2 mm³/s). The latter may require a different hotend to get that flow, but usually it is advised to print slower with a larger nozzle.
Most practical is to use the linear printing speed. This is the value you find in the slicers. But, for a given hotend design it is good to keep the maximum volumetric flow into account to determine whether you are within the specifications of the hotend when you change certain printing/slicing parameters.