It was related to the 'position' of the audio devices attached to my system.
Easiest way to explain it is that when I opened Kmix there were three audio devices listed and their respective sliders.
First was my Video Cam and the slider for the MIC,
next was my sound card and all the various sliders related to that, and
third was my wireless headset and its relevant sliders.
It appears that the audio from the flash video was being sent to the first listed device (the webcam) and not to the soundcard!!!!!!!!!!!
I unplugged the webcam, rebooted, checked that the sound card was now the first listed device, plugged in the webcam, and it became listed as the third device now, not the first.
Sound now works for flash videos in Konq and Firefox.
Man was I puzzled for quite some time .......... but all is well again!