About 80% of flare originates with the subject, but it only exists when there's an optical system involved. There are a couple of different types of flare, veiling has to do with the optical system and camera creating an evenly distributed level of exposure. Another type is ghost which produces an image of the aperture.Regarding the sources of flare in testing etc, again, I'm refering mostly to flare caused by the subject/test target, not the lens. The kind of "veiling" lens flare Adams refers to is likely a relatively minor issue with most contemporary lenses.
While flare plays a factor in the determination of film speed, for me it's more about the effect it has on the illuminance range. Kodak's contrast index for normal processing contains a value for flare. Their numbers won't work without it.