fully charge and hold down the button for 30 secs ... this has helped with my own device. also depending on how long you've had the kindle... check out the recent recall for chargers that were said to have problems. theres a serial on the side that can be quoted to be sure its not included or can be replaced for free.
http://news.sky.com/story/1652016/kindle-charger-recall-over-electric-shock-fears