Can a flexible flue liner be installed in an old central heating flue for modern HVAC systems?
Yes, a flexible metal flue liner can often be installed in an old masonry flue. In fact, I had one done last year, where we had an old (wood-burning) fireplace and installed a gas-fired log fireplace insert. The contractor threaded the two flexible pipes down from the top -- one for combustion air and one for venting the exhaust.  Many modern boilers also have the option to use a sidewall power-vent, which doesn't need any flue at all -- just some PVC pipes.

There are numerous suppliers of flexible metal chimney-liners.