There certainly was a flying club at Kai Tak, but not sure if there is one at CLK. It's just possible they're at Sek Kong (the former RAF base), although at least one of the runways there is long since cut in half. Whichever, unless you're out there for a long time you're not going to be able to go solo, and be prepared for a shock with the price. It was several hundred quid/hr for a C172 last time I checked, & that was a few years ago.
ap.
Further to this; $1798/hr dual C152 which is roughly £180/hr. There are also joining fees involved.
Look here:
http://www.hkaviationclub.com.hk/course_offer.htm