This is not just happening to you but many it has happened to all my family and friends since the latest update occurred it isnt your charger or wires as it is happening to 16 ppl i know all at the same time plus many others online, i read that resetting the phone helps but im not to willing to do that just yet. Perhaps they put a block on non genuine apple products? I can get mine to work after taking it out and putting it back a few times. I just noticed this post is very out of date but anyone searching for answers on this question now it will be useful
To fix the problem where the iPhone charger says accessory not supported, you need first to reset your iPhone. This will ensure that all updates are erased and old settings retained. You can also try removing the pairing kit in the iPhone and then try to repair the phone.