On Kali Linux, flatpak can be installed through:

kali@kali:~$ sudo apt update
kali@kali:~$
kali@kali:~$ sudo apt install -y flatpak
kali@kali:~$
kali@kali:~$ sudo flatpak remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo

It is also a good idea to install the Flatpak plugin for GNOME Software. To do this, run:

kali@kali:~$ sudo apt install gnome-software-plugin-flatpak

Now you can install new flatpak apps from the software center.

If you want to make flatpak apps look more consistent with the system you can force them to use your local themes:

kali@kali:~$ mkdir -p ~/.themes
kali@kali:~$ cp -a /usr/share/themes/* ~/.themes/
kali@kali:~$ sudo flatpak override --filesystem=~/.themes/

• Flatpak
• Debian Quick Setup