The Duchess of Kent was photographed on two separate occasions wearing the same dress and necklace in 1969: during the Kents Australian tour of August 1969 and at a theatre in London in late October 1969.
London 20 October 1969
In this photo from the same occasion, a glimpse of the rear of the necklace can be seen.
The Duchess also wore the necklace in Australia in August 1969.
Both details are from the same occasion. Sorry that the images a bit more than blurry!
I have never seen any information about the origins of the necklace, nor have I noticed it on other ladies in the Kent family.
Some how I very much doubt if it belonged to QEII or was a gift from the King of Saudia Arabia, as I don't think that the Duke and Duchess ever made an official visit there. But that is all just speculation on my part.