When animating, I realised not all the key frames get flipped! After selecting a column of keyframes in the dopesheet, I press Ctrl+C to copy them, then Shift+Ctrl+V to paste/flip them, but only one keyframe is flipped and the others are not. Why?
Based on this other answer (which might be helpful), it sounds like you're expecting Blender to do something that it's not designed to do.
(Making some assumptions) I think you're trying to flip the keyframes of more than one channel or object at a time, which doesn't seem to be possible. If that other answer is any indication, you can only flip certain sets of keyframes at once (probably per-channel or per-object, but I can't experiment right now), and you'll have to do the others manually.
Whenever I've had a selection problem in the Dope sheet, I've had to revert to using "A "first to deselect anything that might be highlited already, then "B" to Box Select the required keyframes, and when only the required keyframes are lit up, press CTL-C, then CTL-V. I've only ever done this with keyframes related to the one object, never over separate items in the 3D window.