iPhone 6+ charging "Accessory May Not Be Supported" error.
I had the exact same problem with my new iPhone6+. I played around with it a bit and noticed that it would charge, albeit very slowly, if I turned it off while plugged in. At the same time, I received the same error message when connected to my computer, although the data connection worked perfectly. If I turned the phone off while connected to my computer, it also charged very slowly.
I tried the same cord and block with an iPhone5, and it worked with no problems. I tried the iPhone5 cord and block with my new iPhone6+ and it did not work.
I tried both soft and factory resets, and neither fixed the problem.
I took it to the Sprint store today, and they informed me that it was not reparable. Because it is the 64GB version, none were in stock, so they have to return the phone for an exchange. They suggested that I try to go to an Apple Store, although the odds that they had a replacement in stock were also slim to none.
It was described to me as being an "out-of-the-box defect", though none of the employees in the store had seen this problem before. They couldn't explain the cause of the problem either.