I used this every time (with sudo):

#!/bin/sh
[ "$USER" != root ] && { sudo "$0" && exit; }
latest_version=$(
  curl -sI 'https://discord.com/api/download?platform=linux&format=deb' \
  | grep '^location:' \
  | grep -m 1 -oP '\d[\d.]+\d' \
  | head -n 1
)
sed -i.bak 's/\(version.*\)[0-9]\+\.[0-9]\+\.[0-9]\+/\1'"$latest_version"'/' \
  '/usr/share/discord/resources/build_info.json'

Let's see how good the Flatpak version will be.