If anyone needs steps with the CCK for transferring from iPhone 4 or 4S:
Plug in kit to phone and iPad. Your iPad should automatically open and display all your phone's photos onscreen, as thumbnails. On iPad, it will say Delete All and Import All at the bottom of your screen. You click whichever photos you want to import. It will let you know if your iPad doesn't have enough space. Once you've copied the photos of your choice, you will be asked whether you want to delete the photos from your phone. Whatever photos you've imported to iPad will be in an album named Last Import. If you import again, those earlier imported photos will end up in an album called All Imported.
I've not tried moving those imported photos around on iPad among albums, so have no details about that.
I originally bought a CCK to use with my digital camera, but it turned out my camera is so old it's not supported. And my iPhone 4 actually took better photos, so I ended up using it as my camera and my iPad to display the ones I like. I took about 2,000 photos on one trip, didn't want to scroll through on iPhone to show off a few, so I transferred them to iPad. No Internet or PC was involved in transferring; just iPhone and iPad, and CCK, of course.
By the way, I've tried with my iPhone 4S. Works fine, too.