There are several ways to measure flex on a sword. The SCA uses a method where they dangle a weight from the tip of a sword and measure how far down the sword flexes. This means that whomever does this must possess the exact weight needed and have a set up where they can clamp the sword and easily measure the change in distance that the sword moves.
There is an easier method that is becoming standard in Historical European Martial Arts (HEMA).
Most people have a weigh scale. If not, it’s often easy to borrow one. some schools even keep one on site at their practice hall. Thus, using this as a method of testing flex is easy and reliable, as long as the scale is reasonably accurate. This is the method that Sword Gear uses. Simply press the sword into the scale until it reaches its maximum flex, and record that number.
Current standards for flex are a maximum of twenty kilograms for longswords. This should be less for shortswords, of course, but I haven’t read any conclusive standards on this. Whenever flex is shown on sword on Sword Gear’s site, this is the way it is measured.
For a comprehensive analysis of sword flex, read Sean Franklin’s article Standards For HEMA Testing – Everything You Ever Wanted To Know About Blade Flex.