I'm not 100% sure about Kindles as I haven't owned one, but Nooks use a modified Micro USB, it's not quite the same
Kindle might do something similar. I can't plug any of my generic Micro-USB cables into my Nook, they fit fine, but they aren't long enough to stay attached, you have to hold them in place. They *might* stick if you removed the plastic casing to make the connector longer, but I haven't jacked with it, I've just kept using the cord that came with the Nook.
I have a lot of random Micro USB cables (HTC cords that came with my EVO, Samsung cords that came with my S2, generic cords from monoline, etc) and they seem to all be slightly different lengths because of differences in the plastic casing. They all work with all my phones just fine, and my Nexus 7 just fine, but none work with the Nook.