1) hyphenate epub
2) convert epub to to "dual" /"combo" mobi format (change "Mobi file type" option from "old" to "both", in Mobi output tab)
3) email (or use Send to Kindle app) that mobi file
4) your Kindle should download an azw3 "part" of that dual mobi file you've send, and it will have soft hyphens.
If for some reason Amazon sends old mobi format when you use Calibre to generate "dual mobi" then try using
kindlegen (or Kindle Previewer, it also uses kindlegen) for that epub> mobi step (kindlegen by default produces "dual"/"combo"/"master" mobi file).