Hello, my name is Rusty. The first generation Kindle (D00611) uses a standard Micro USB charger. Yes, they are available, click here. This one comes with a USB charger, so you can use it with other devices as well. If you have a charger that fits (perhaps in a box of extra cords), it's the right one. They only make one type of charger for that connector.
You can get one online at this link, click here (sorry, forgot to include the link), or you can get one at any electronics store, or even some gas stations carry them. It's called a MICRO USB charger.