I have just added this to the map of places to fly your drone at Drone Scene:
Land owner permission requirements unknown.
The guys that built Stonehenge picked a very bad site for drone flying.
The Larkhill danger area almost covers the monument itself and much of the land not under flight restriction or military air traffic zones is owned by the drone-unfriendly National Trust.
The take off / landing point I have marked is on a BOAT, specifically AMES12, Wiltshire County Council designated Byway Open To All Traffic. So you can legally drive either north or south of the A303 on the byway,
I chose the southerly part of the byway. 80 metres from the A303 there is room to both turn a car round and to park it to the side of the byway. The northern route would presumably be as easy but it brings you closer to what may be over-zealous security. The BOAT can be seen in the short video (taken for a Grey Arrows competition)
There is a very useful thread on Grey Arrows started by ianinlondon about flying around the Salisbury Plain monuments.
If you do go probably best to check the sunrise / sunset times and the times the monument is open. A golden hour flight without people in shot could be a nice experience!
The originator declared that this location was not inside a Flight Restriction Zone at the time of being flown on 09/08/2020. It remains the responsibility of any pilot to check for any changes before flying at the same location.