Please pardon the brevity of this post if you are instead looking for long replies with multiple links to multiple documents, some of which have nothing to do with your issue.
Apple will not offer repairs on the port on your iPhone 6 Plus, basically leaving you with the choice to buy a new or refurbished phone.
It might worth considering a 3rd party shop that is willing to repair or replace the port on your iPhone. The downside......Apple will likely refuse to work on the phone at a later time because of service performed by an unauthorized repair shop. On an old phone like the iPhone 6 Plus, you really are not risking a lot here though.