The way I have it, is that I copied org.kde.plasma.browser_integration.json from /usr/lib/mozilla/native-messaging-hosts/org.kde.plasma.browser_integration.json (for Kubuntu 22.04, might be elsewhere for you) to ~/.var/app/org.mozilla.firefox/.mozilla/native-messaging-hosts and then changed the path to a shell script that calls the original executable with flatpak-spawn --host. Of course this kind of breaks sandboxing since you are allowing the browser to access programs on your machine but it works.
So I have:
org.kde.plasma.browser_integration.json :
{
"name": "org.kde.plasma.browser_integration",
"description": "Native connector for KDE Plasma",
"path": "/home/username/.var/app/org.mozilla.firefox/.mozilla/native-messaging-hosts/org.kde.plasma.browser_integration.sh",
"type": "stdio",
"allowed_extensions": ["plasma-browser-integration@kde.org"]
}