Hopes of a return at Twickenham on Saturday for talismanic fullback Stuart Hogg have also been quashed.
Seymour suffered a rib injury as Scotland lost 18-11 to Wales at Murrayfield on Saturday with Kinghorn sustaining an ankle injury in the same game.
They add to a significant injury list in this year’s competition for the Scots, who began with a win over Italy but then lost to Ireland and France as well as Wales.
Hogg has been missing since going off against Ireland in the second round and has not recovered in time, Scottish Rugby said.
Ruaridh Jackson and uncapped Kyle Steyn have been called into Gregor Townsend's squad as cover with Scotland seeking a victory at Twickenham for the first time since 1983.
Townsend is already without experienced loose forwards John Barclay and Ryan Wilson plus centre Huw Jones.
(Reporting by Mark Gleeson; Editing by Ken Ferris)
