Finally discovered the reason for the slow framerate and stuttering on my Kubuntu Linux. It seems that the problem is to do with using the windows composite manager compiz-fusion. Whilst looking for a solution I stumbled across this on the Ubuntu forum. This led me to this very useful article about Flash Optimization.
Although there are a number of suggested fixes at this site I tried the simplest - I installed fusion-icon and then used it to change the window manager to kwin.
I replayed a couple of online flash videos that had been playing really badly and, hey presto, the frame-rate was much improved.