The teenager claimed a pipe bomb had been planted on the premises.
NCA investigators, working with the FBI, also found that while on bail for the bomb hoaxes, Duke-Cohan had made a fake report of a hijacked US-bound plane via phone calls to San Francisco Airport and police.
He claimed there was a bomb on board flight UAL949, which was travelling from Heathrow to San Francisco with 295 passengers.
Jailing him, Judge Richard Foster said: "You knew exactly what you were doing and why you were doing it, and you knew full well the havoc that would follow.
"The scale of what you did was enormous," the judge was quoted as saying by the report.
His defence barrister said psychology experts had described Duke-Cohen as very immature, but the prosecution said he craved attention from his followers on social media.
Marc Horsfall, senior investigating officer with the NCA, said Duke-Cohan had few real friends and spent "a great deal of his time online".
He had no previous convictions and lived with his mother and sister.
However, he was linked to a cyber-hacker group on Twitter calling itself the Apophis Squad - and developed a number of online aliases.
In January 2018, the IT student was expelled from West Herts College for issuing a bomb threat.
His first bomb hoax email was prompted by a disagreement with the owners of VeltPvP, a US-based server that allows users play the game Minecraft.
Duke-Cohan was annoyed at not being given access to higher levels within the game, the NCA said.
More than 400 schools across the UK were evacuated before the email was dismissed as a hoax.
Duke-Cohan was arrested at home within two days, and his laptops, USB sticks and mobile phones were seized, the report said.
(With inputs from agencies.)