Are your CJK fonts installed at system level or as user files?
If at system level, I wonder if it could be because the flatpak doesn’t have permission to read the font files. Might be worth using the Flatpak permissions KDE module to give read only access to system files, just to see if that changes anything.
If not, have you tried with another flatpak browser, e.g. Zen?
It might be because Flatpak is not exactly well-made for non-English, I only speak English though. I would try installing your browser as sudo. I really liked Flatpak before but it never respected my GTK theme, so I barely use flatpak. Not so sure though. I think it might just be a flatpak issue. If this still happens when installing as root, then it might be a Chromium issue.
They are installed at system level. I have tried to copy the fonts (including the CJK ones) from /usr/share/fonts to ~/.local/share/fonts and give access to that directory to the flatpak via Flatseal.
I’ve just tried with Zen, installed as a flatpak and the characters render as expected.