It sounds like you've already done the basic troubleshooting of using a known good Apple OEM charging block and cable---this is an important step!
Your next step is to troubleshoot the charge port itself---these things are exposed to the external elements and can often become corroded or dirty over time. Try cleaning the charge port with 99% isopropyl alcohol on a q-tip. Ideally, you'd do this with the battery disconnected, or have the Apple Store if convenient, or a quality independent repair shop do this for you.
A great little tool for diagnosis of charging issues is an inexpensive usb ammeter on Amazon. If you plug your phone into the ammeter and the ammeter into the charger, you'll be able to see the amount of current your phone is pulling. This will help you troubleshoot a bad cable or bad connection as you wiggle it around. An iPhone 6 should pull about 1 amp of current for normal charging of a low battery.
If that doesn't work, then the next step is to actually replace the charge port with a known good, and if no joy that points to a problem with the charging logic chip--the tristar chip on the board. This chip is very sensitive and is easily damaged by use of non-Apple chargers, especially car chargers. This chip can be replaced by the better independent repair shops, or as a mail in repair. Apple will not address board level repair for iPhones.
Of course if all that sounds like a pain, you always have the option to go to Apple and just pay the $299 Out of warranty swap fee to have them replace the phone for you.