OSTYPE

OSTYPE variable stores the value of the operating system type.

echo $OSTYPE

linux-gnu # Ubuntu

zsh and bash values differ a bit.

bash

$ echo $OSTYPE
  darwin18

zsh

% echo $OSTYPE
  darwin18.0

You can use a glob to account for the inconsistency

if [[ $OSTYPE == darwin* ]]; then
alias flushdns='sudo dscacheutil -flushcache'
fi

Another code snippet from the virualmin install script

remove_virtualmin_release () {
  # shellcheck disable=SC2154
  case "$os_type" in
    "fedora" | "centos" | "rhel" | "amazon"	)
    run_ok "rpm -e virtualmin-release" "Removing virtualmin-release"
    ;;
    "debian" | "ubuntu" )
    grep -v "virtualmin" /etc/apt/sources.list > "$tempdir"/sources.list
    mv "$tempdir"/sources.list /etc/apt/sources.list
    ;;
  esac
}

uname -s

-s prints the kernel name

Linux # Ubuntu