St Peter's C of E Junior School closed in December after rot was found in its timber structure.
Initial work to move utilities and telecoms will start next month and last into next year.
Oliver, 13, and Edward, 11, will travel to California for the Pokémon World Championships this month.
The Lincs and Notts Air Ambulance charity says the site is "essential" to help meet demand.
The owners say the carriages were "highly significant" in an early attempt to open up train travel.
Flying Scotsman is back on the railway where it ran passenger services in the early 1950s.
Pupils have been reunited three months after their old school was suddenly closed.
St Peter's C of E Junior School in Ruddington was forced to close in December over safety concerns.
St Peter's C of E Junior School in the Nottinghamshire village closed over safety concern last year.
