Flight visibility is generally defined as “the forward visibility from an aircraft in flight”.
As a result, it’s normally only the operating crew who can decide what their flight visibility actually is.
Ground or “Met vis” (Meterological visibility) is normally measured by a competent observer (can be ATC or a Met person) by seeing which landmarks are visible from the tower. Certain buildings, hills, even conspicuous trees will have had their distances accurately measured and the observer will ascertain which of these are visible at the time of observation.
For Runway Visual Range (RVR), this is now measured automatically by transmissometers and is normally only reported when the RVR is less than 1500m.