Strange, works here. I'm using DeJavu Sans Mono fonts in Kate and System Settings if that matters.
I have the same problem. I changed the font, then it worked for a while. Now it doesn't. The menu has it checked, saying it should be working.
I've toggled auto spell-check, changed the font, and re-started Kate several times. Nothing seems to work.
Auto spell-check should work in any font. Is anybody here as frustrated as I am?
In my case, it turned out to be a problem with the screen scaling. I have a high DPI screen and I've used 1.5 scaling factor for the screen. It messed up the underlining of the misspelt words.
I've reported it here:
https://bugs.kde.org/show_bug.cgi?id=383922
