Medway and Maidstone are the main club, but they are an athletics club rather than a typical running club.
I am not aware of any other club in Medway - certainly there SHOULD be one.
Otherwise you can travel to Gravesend (Gravesend Road Runners and Ifield & Istead RC) or Maidstone (Maidstone Harriers - my club).
Lots of good running in Medway though - whereabouts are you based?