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BabySnake wrote on 10/09/14 at 10:26:15:

(I have tried chess ebooks mostly on just my Android smartphone, an HTC One m8.)

Forward Chess interactive ebooks are authored in ChessBase. Forward Chess then encrypts them (I think) to make them proprietary (something like that).

Gambit and Everyman each also have their own interactive chess ebook format. I suspect that ChessBase might also be the authoring environment for these two ebook formats.

(I think 'New In Chess' also has an ebook format, but it is restricted to Apple devices.)

The Forward Chess app could be improved, but IMHOpinion the Forward Chess app is the best of the three interactive chess ebook apps; with Gambit being the next best.

One strength of Forward Chess is that it is available to all publishing houses that want to use it, probably including good quality "self-published" chess ebooks written by amateurs.
I do not know whether Everyman could publish its interactive chess ebooks in both their own format plus on Forward Chess, but I suspect the dual publish would be acceptable to Forward Chess.

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The noninteractive Kindle format is not obsolete for chess ebooks. The Kindle format has one major strength over all the others: Kindle has the concept of a pre-determined 'page'. For example...
One swipe takes you to a page that contains a shot puzzle diagram and asks you to find the shot move on your own. The next swipe takes you to a page where the diagram is repeated and the answer moves are given.

For a smart common sense design for a chess ebook on Kindle, see John Nunn's 1001 Deadly Checkmates.

However, it is unfortunate and surprising that a some chess ebooks for Kindle were designed with no apparent effort at engineering a good experience for the user: for instance, you can risk your money on the Kindle edition of the newly updated algebraic edition of Fred Reinfeld's classic 1001 Winning Chess Sacrifices and Combinations.
Compare the Kindle update of Reinfeld by Bruce Alberston -to- John Nunn's checkmates Kindle ebook, and you will see which design is much better than the other.

One drawback of the Kindle format for chess ebooks, or any ebook that relies on images, is that the image size does not automatically tune itself to the available screen size of the device. As a result, on smartphones the images, including 2D chess position diagrams, are usually unpleasantly small.
You can double-tap the image to temporarily overlay the Kindle page with a larger display of the image, but that is tedious and it overlays whatever chess moves might be important for the diagram.

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What ebook readers/formats for chess books do there exist?

I know of e+books (only work on ipad/iphone I believe).

And Forward Chess (work on android/ipad/iphone/PC).

Are there more? I also know of cbv files for Chessbase/Chessbase viewer which can be nice but that's slightly different in my view, I am thinking about something that works on a smartphone.

What is the actual format/files that these readers use? (Forward Chess and e+books). And any other smartphone chess apps?