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?
Select the keyframes in the dope sheet editor, than - Shift+M (in the menu: Key - Mirror)
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.
You could try going to the Graph Editor, selecting all of your keyframes with A, and then scaling on the x axis with: s, x, -1, which will invert all of your keyframes. Although this might not work on multiple objects...
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.
The issue is that Blender only flips keyframes where the associated bones have left and right pairs. For
V to work, the bones that flip should be named
Bone.R. If this naming convention is followed, they should flip properly.