A bad battery is possible. If you could either install a known-good battery or charge yours in another device, then you would know for sure.
However, a lot of iPhones suffer from a defective charge circuit on the logic board. That is the Tristar IC (U2) and the typical symptoms when it fails is no-charge and fake charge. This IC can be damaged by hard falls or using non MFi-Certified chargers. Most of the protection circuitry is in the charging bricks Apple sells. The cheap stuff does not have that circuitry so they can induce voltage spikes that damage your logic board.
Try to resolve if your battery is the problem. If not, you will need to find a qualified repair shop that does micro-soldering repairs.
N.B. If, by chance, your iPhone 6 is still under warranty...go to the Apple store !