Here's the 1853 extract from the OPR index at Scotland's People. As he was said to be 84 on 1 February 1853, and if that is accurate, he was born 1768/1769. If it's not accurate, he could have been born a year or three later.
If you think this could be the Robert Kilgour you are interested in, you need to look at the original at
www.scotlandspeople.gov.uk and see whether or not it tells you where the grave is, and/or who else is buried in the same lair.
There is also a burial of Jean Law, 67, in Falkland on 17 September 1840.
In the 1841 census in Falkland are Robert Kilgour, 70; Agness Kilgour, 35; Jean Kilgour, 25; Robert Christie, 14. In 1851 Robert Kilgour, 78, born Leslie, is alone in a house in Falkland.
There's no surviving record of the baptism of a Robert Kilgour in Falkland between 1731 and 1791, but there is a baptism of Robert, son of Thomas K and Elizabeth Greig, in Leslie on 25 April 1773.