Got a pair for my kids at Christmas, 3 and 5 years old respectively. Hardware-wise they aren't great, 1GB of RAM just won't cut it these days, while the software has a few niggles that take getting used to especially when compared to stock. That two year no questions guarantee is a huge plus though, my five year old went through 2 Nexus 7's prior to me going for the Fire. While you might encounter usage problems, your kid will likely never notice, and they are great little media consumption devices with plenty of content freely available through the Free Time feature.
Word of warning, many advise side loading the Play Store to sidestep app availability issues on the Amazon store, but doing so voids the guarantee.