Finally I need all data fields (subject,body etc.) into separate variables to pass it to send a mail.

That isn't necessary. You can use the values directly from the hash. eg:

print MAIL "Subject: $parts{SUBJECT}\n\n";
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See Not Exactly a Hash Tutorial for more on how to use hashes.

As hippo said use the values in hash directly.

#!/usr/bin/perl 
use strict;
use warnings;
my $mailprog = "/usr/sbin/sendmail";

my $file  = 'mailinglist.txt';
open my $fh, '<', $file 
  or die "Could not open $file : $!";

my %mail = (
  'FROM' => 'rahul.agarwal@everyone.com',
);
my $key;
while (my $line = <$fh>) {
  if ($line =~ /^([A-Z]+)$/) {
    $key = $1;
    if ($key =~ /^END/) { 
      undef $key; 
    }
    next;
  }
  next unless defined $key;
  $mail{$key} //= '';
  $mail{$key} .= $line;
}
close $fh;
$mail{$_} =~ s/^\s+|\s+$//g for keys %mail; # trim

#open (MAIL, "|$mailprog -t");
#print MAIL << "EOM";
print << "EOM";
To: $mail{'TO'}
From: $mail{'FROM'}
Subject: $mail{'SUBJECT'}

$mail{'BODY'}
EOM
#close(MAIL);
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