SQL ...

create table test_members (
username varchar(20),
referral varchar(20));

insert into test_members values ('Jack',null);
insert into test_members values ('Bob','Jack');
insert into test_members values ('Joe','Bob');
insert into test_members values ('Henry','Joe');
insert into test_members values ('Gabe','Jack');
insert into test_members values ('Pete','Gabe');
insert into test_members values ('Tim','Gabe');
[download]

Perl...

use strict;
use DBI;

my $database='db';
my $username='user';
my $password='pass';

my $dbh=DBI->connect('DBI:mysql:database='.$database,
                     $username,$password);
print 'dbh error' if (!$dbh);

my @ref = ();
my @names = ('Jack');
my $base_sql=q{SELECT username FROM test_members WHERE referral };
while (scalar(@names)) {
  my $sql=$base_sql.($#names?'in ('.join(',',map('?',@names)).')':'=?'
+);
  print "$sql\n";
  my $sth=$dbh->prepare($sql);
  print 'sth error' if (!$sth);
  my $rv=$sth->execute(@names);
  print 'rv error' if (!$rv);
  my $res = $sth->fetchall_arrayref();
  @names=map($res->[$_][0],0..$#$res);
  push @ref, join '|',@names if (scalar(@names));
}

print join(',',@ref),"\n";

print "finished\n";
[download]

Should do the job

Hope it helps
UnderMine

Update: username and referral were swaped around.. think referral should be called referrer