An article on overhauling the carbs on a Ford 8N tractor says to use a flare nut wrench to disconnect the fuel line. How important is it use that kind of wrench, vs. an open ended wrench?
Using a flare nut wrench (aka line wrench) should be used if it is calling for it.
The reasoning for using a flare wrench over an open ended wrench is that you can grip all sides of the fitting just like you can with a box wrench but the opening at the end of the wrench allows you to slip over the connected hose/line unlike a box wrench.
This allows you to apply more torque with less likeliness of slipping and rounding it off.
Depending on the size and material the fitting is made from, it can be very easy to round off, the flare wrench lowers that chance.