I have an iPhone 6s Plus. The lightning plug port had stopped charging – sort of. The plug wouldn’t stay in and I would have to carefully hold it “just so” to get it to charge. I had the same problem with my original iPhone 5s. It was the reason I upgraded to the 6s Plus.
So I called my local Batteries + Bulbs. $80 to replace the charging port. BUT the nice lady I spoke to suggested using a toothpick to clean out any lint. I used a toothpick and compressed air (computer dust spray) and cleaned out a fair amount of lint.
The charging plug snaps briskly in and charges. Son’s iPhone … same problem … same solution.
PS – I also cleaned out my old iPhone 5s … problem solved.