not within the Dockyard itself but part of Chatham’s defences in conjunction with Upnor Castle.
it was constructed in 1756 at the southern end of the Brompton Lines to protect the southern approach to the historic dockyard . It was built following the Dutch attack that destroyed many vessels in 1667.
During the Napoleonic Wars the defences were and considerably strengthened using convicts from St Marys Island .
Its the most complete Napoleonic fortress in Britain and as such was scheduled as an ancient monument in 1959.
More information is available on Wikipedia here
The Fort is open to the public for tours , tickets available from their web site here
There is information on their halloween event here
quote :- Fort Amherst’s annual Halloween Horrors have been described by the experts at Scare Tour UK as ‘not for the faint of heart’ and as being ‘like something straight out of a horror film!’ by What’s On magazine… and they are as terrifying now as they have ever been! However due to the overwhelming success of events suitable for our younger guests, we’re proud to announce that children’s and teens tours will again be available for 2016!