Via https://www.emacswiki.org/emacs/FlySpell#toc9 and https://www.reddit.com/r/emacs/comments/4oc7pg/spellcheck_flyspellmode_underlines_disappear_when/d5l9vtt/ I found this solution:

(defun flyspell-buffer-after-pdict-save (&rest _) (flyspell-buffer)) (advice-add 'ispell-pdict-save :after #'flyspell-buffer-after-pdict-save)