I have a Boyue Likebook Plus and do virtually all my reading through the kindle for android app. It works fine. I miss page turns now and then, so have to swipe twice, but I suspect that's more an issue with the firmware/touchscreen than it is with the kindle software.
Kindle does work better on an actual kindle: it's more responsive. Still, that shouldn't surprise anyone. I've always thought Kindle for Android works well enough. For now, I like having a 7.8" e-ink screen, more than I like the slightly snappier feel of reading from a kindle.
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