I am having the same problem, and I have a workaround to offer, at least for Linux systems. The directory where Brave stores its dictionaries is:
~/.config/Brave-Browser/Dictionaries
On my system, that directory is empty. However, I have both Chromium and Chrome installed, and they have equivalent directories with dictionaries:
~/.config/chromium/Dictionaries/en-US-9-0.bdic
~/.config/google-chrome/Dictionaries/en-US-9-0.bdic
I copied the file, “en-US-9-0.bdic” to the “Brave-Browser/Dictionaries” directory, then restarted Brave, and spell checking started working.
I have tried this on Linux only. Hope it helps!