According to the PHP documentation on link :
int mysql_affected_rows ([ resource $link_identifier = NULL ] )
This is a function that returns an integer value containing "the number of rows affected by the last INSERT, UPDATE, REPLACE, or DELETE associated with link_identifier ."
link_identifier : in turn is the connection to the mysql database. This argument is not required when you only have a MySQL database connection.
Bringing this to your example would be:
$conexao = mysqli_connect("localhost","root","","banco");
$nome = isset($_REQUEST['nome'])?$_REQUEST['nome']:"";
$telefone = isset($_REQUEST['telefone'])?$_REQUEST['telefone']:"";
$sql = "insert into tb_banco(nome, telefone)values('$nome','$telefone')";
$salvar = mysqli_query($conexao,$sql);
$registro = mysqli_affected_rows($conexao);
if($registro==0){
echo "telefone já cadastrado,use outro";
}else{
echo "Cadastro realizado com sucesso";
}