Spelling does not work by default. If you enable spelling then change the dictionary from the default USA (GB) English, to GB English, the spelling comes on. You have to do this with every document. Reproducible: Always Steps to Reproduce: 1. install a UK KUbunu distro 2. open Kate and type some incorrectly spelled text, click tools, click spelling. 3. not no spelling check is done. 4. open dictionary at foot of window, change to GB English, now it works.
Please try a recent KF5 version (e.g. neon.kde.org). If that still fails there, please report problem to frameworks-sonnet. For me that works on archlinux, but that might be distribution related.