So, I've gone in and tested this with three different devices at work, with three different cables. (iPad Air, iPad 2, and IPad mini). All three have issues charging from an Amazon Certified Lightning cable via a wall charger. Swap the cable to an "official" Apple cable and the issue goes away. These are not counterfeit cables and all three cables worked fine to charge the SAME devices prior to iOS 10 updates (which, by the way, bricked one of the devices, but was recoverable with a full factory restore and install) with exactly the same charger.
Oh, other bits of info, these same cables and charger have no issue charging multiple iPhones (5c, 6, 6s, 7, and 7+) with iOS 9 or iOS 10. There also seems to be no physical defects of any kind with the cables, no wear at the ends, no sheathe showing internal wires, etc.
This tells me that Apple has some sort of logic going on in iOS 10 to check for chipped cables and it's buggy. I'll bet you that this "issue" will magically go away in the next couple of updates.