do I need new battery
Flashes amazon when unpluged works when pluged in.
Released July 24, 2014, Amazon's Fire Phone is Amazon's first smartphone, designed to compete with iOS, Android, and Windows Phone devices.
If you bought the phone two years go and have used it frequently I think you might need a new battery since I have switched battery fro most of my phone between year one and two.
You will need a battery like this
from the ifixit guide.
Search for the PN number on any sales site like e.g. ebay