Would this bag be good to hold 1 or 2 binders for high school?

If you're worried about it not fitting then spend the extra $7.00 and get the 17"×13"×4" size, it will fit a laptop or tablet, 1 or 2 binders and a book or two. It's absolutely worth the extra money!!

can this fit a 15.6 inch laptop?

I have a 15.6" lenovo, it's about 1" too big to fit all the way inside, so it hangs out of the top of the bag a little. I just extend the straps and fold over the flap to hide it. Looks ok, but probably should get a bigger one.

How would this be for storing a kindle, books ands a few chargers?

It would be fine. If it's not huge textbooks. If they are just little leisure books and the kindle and chargers it will be more than enough room

How deep if this bag, i.e., front to back? The product page is woefully short on dimension details.

I purchased the bag to use as a "purse". It is not very wide, but depending on what your using it for it may be enough room for you. I personally Love it, even with limited space. I generally carry alot in my purse and I was able to pack it all in. The pockets on the front and sides were a big help for keys and cell phone. Again, not much room, but it all depends on how your planning to use it. Thanks