onesojourner:
So are you saying the chip would see the 12.6v?
Yes, and it won't charge. It may even fry that chip. (haven't checked the ratings)
Can the input to these boards all use the same 5v source provided it there are enough amps?
Absolutely. Even if there aren't enough amps it will work by charging at a lower current.
Can I run all three outputs in parallel and then step up the 4.2v to 12v?
It should work. Although that 4.2v will soon drop back to 3.7v.
I am trying to build a simple solar powered 18650 powered light.
maybe you should tell more about your pproject and we can help you find the best solution.
There are better options, You could use a 19 or 18v laptop battery pack. It has a built in balancing circuit. You just have to step down the voltage to 12V.
Or
you could use a DIY powerbank kit like this which could charge multiple 18650 cells without any problems.