It's been a while since I've sideloaded books into the Kindle app, but assuming no DRM on the files, I used to email a file to myself & then use "open in..." on the attached file from the email app to move the file into Kindle. There used to be a documents folder in the app bundle, but I'm not seeing that in iFile on 8.1, so I'm not sure where they're hiding that now for sideloading directly nowadays.