This could mean one of two things:
- You plugged your iPhone into an accessory that Apple has decided to no longer support with your current device. If the accessory doesn't send appropriate authentication code to the iPhone, or the code is not on the 'approved' list, it will display "Charging is not supported with this accessory". How to resolve this? You can't, yet, but there are some options for getting video out to other devices that are no longer supported using a program called ReSupported by Phoenix-Dev.
- Your device (iPhone/iPod/iTouch) has damage to it and flashes the "Charging is not supported with this accessory" over and over. This is usually caused by impact damage or fluid/ water damage to the bottom dock and can be fixed. This is caused by corrosion that builds due to moisture and spreads like a mold along copper circuitry, which when contact is made between two points that aren't intended to, the device thinks that there is an accessory is plugged into the bottom dock. If the 'accessory' doesn't send an authentication code (obviously it won't because it's just corrosion), the device rejects it as an approved device, but still thinks something is plugged in, thus the persistent "Charging is not supported with this accessory" or "This accessory is not made to work with iPhone"