No, it does not have to be a Kindle product, but I would be careful. It is a fairly standard interface, and if you want another adapter, I highly recommend the iGo, available in lots of places including Amazon and RadioShack. The iGo adapter has various interchangeable tips, there are tips for literally every small device out there. I have tips for my Kindle, Sony camera, iPods, Palm Treo, Nintendo DS, and old unused Motorola Razr.
The charger package I purchased has two cords, and can power two devices simultaneously. It has connectors for standard outlets, auto and airplane. It is the only thing I take when I travel. The tips are sold separately, and run from about $3 to $12 depending on where you get them. I have so many of the little tips that I have labeled them for each device.
http://igo.com/