Can't add user to docker group

You need to reload your shell in order to make the changes take effect.

To avoid starting a new shell you can run.

exec su -l $USER

This will create a new subshell with the loaded changes and replace your current shell with it.

Another way is to change your primary group with

export my_group=$(id -gn)
newgrp docker
newgrp $my_group

You can also look at the offical documentation here https://docs.docker.com/engine/install/linux-postinstall/