The flatpak version of Libreoffice Writer can't use Hunspell to do advanced spell/grammar checking (the one with blue underlines). It can load dicts and highlight wrong words with red underline, but not more complex mistakes. This verification works using languagetool, but to use that the user must depend on an online service or setup a local server. Both options are not that great. The expected behavior would be to install dictionaries and have the Hunspell checker working out of the box. A possible solution would be to bake Hunspell into the flatpak package (not a big program) or require direct access to the system package and files for it.
Check the advice here: https://github.com/flathub/org.libreoffice.LibreOffice/issues/62#issuecomment-445863526 If it doesn't help, report it in the flathub issues.