Do Chinese customs agents check the contents of Kindles and notebooks?

No, they won't. Unless they have specific reasons (such as a tip-off) that you are trying to smuggle illegal materials (porn, propaganda etc for distribution in China), they will not care about this. They primarily focus is on security-relevant issues and items for which you need to pay duty.

I never in my life had anyone check documents, laptop, cellphone or laptop contents in a routine check, anywhere in the world.

Of course, if you make trouble at the border and they take you in, they might check everything they can.

I crossed into China last year overland, it was a small border crossing and the border guards had a lot of time and took their time to look through things.

There were a bunch of people crossing with me and in no case did the guards look at the content/data of Laptops, tablets or e-readers.

What they did however is spending some time at looking at photos on pretty much every digital camera. I had crossed several other borders before and had placed a dummy memory card with just a few photos in my camera. With other cameras they spend several minutes at looking at photos. Not that they were really looking for something, they were just curious.

I didn't have any paper notebooks, but I didn't see them looking through any of those in other people's luggage.

Of course turning on a camera and looking at photos is much easier than starting up a laptop and asking for a password.

I've only been through customs at Shanghai and they've never looked at any of my electronics. I've always been carrying a laptop, in recent years I've always been carrying a DSLR (although the memory cards have always been basically empty--I copy the pictures off soon after I take them. This has nothing to do with customs) and a Kindle.

Each year there are ~ 55 million inbound international tourists visiting China, the US has 66 million. Source: World Tourism Organization (UNWTO)

It's neither feasible nor necessary for the government customs authorities to examine your books and electronic devices unless you act really suspiciously.

I'm not saying that it's impossible for them to do that, it's just highly unlikely especially if you arrive at big airports like Beijing or Shanghai. And there's no customs check before domestic flights, you still need to pass security screening though, but the content of your books isn't their concern.

The answer is probably not - but I would think of ways you can minimize your risk.

Each time I enter Shanghai Pudong the border agent checks my visa, doesn't say anything, and lets me through. Then there doesn't seem to be a customs check at all typically (there's sort of an area that looks like you'd set up a queue there, but it's just unattended and I walk out the "nothing to declare" doorway).

I've also entered through Shanghai HongQiao and there was your typical X-Ray machine that you see at subways and at the train station - nothing anywhere near as thorough as the TSA. People barely stop walking to use these machines.

I imagine it could happen. If you can remove those Kindle books from your list temporarily, maybe that's a good idea.

Note that I didn't check bags. One wheeled bag, one backpack.