iPhone 6 only charges at certain angle

Hello,

Try the steps in this article:

If your iPhone, iPad, or iPod touch won't charge - Apple Support

If your device still won’t power on or charge, take your device, charging cable, and charging adapter to an Apple Retail Store or Apple Authorized Service Provider for evaluation. You can also contact Apple Support.

I suspect there may be something blocking the charging port, or there is a problem with the cable. Use a strong flashlight and magnifying glass to look into the port, and use a small, wooden toothpick to remove any dirt, lint, or other debris. See if that helps.

If that will not help, then do as Gus has suggested, make an appointment at the Genius Bar.