#! perl -w scipt

use strict;
use warnings;
use DBI;
use DBD::ODBC;
use File::Copy;

my ($data_source, $database, $user_id, $password) = qw( *********** **
+******** ********** ******* ); 
my $conn_string = "driver={SQL Server}; Server=$data_source; Database=
+$database; Trusted_Connection=yes"; 

my $dbh = DBI->connect( "DBI:ODBC:$conn_string" ) or die $DBI::errstr;

my $Request_id;    

my $Variable_number;    
my $Variable;
my $Choice;
my @VARIABLE;
my @CHOICE;
my $Command; 
my $Return_results;
my $Component_number_old = 1;
my $Component_number = 1;
my $SPROC;
my $unique;
my $elements_in_array;

my $flat_file = "Flat_file.txt";
open (FLAT_FILE, "<$flat_file");

while (<FLAT_FILE>){
  chomp;  
  $Component_number_old = $Component_number;
  
  if ($_ =~ /SPROC\sName\:\s([a-z|A-Z|0-9|_]{1,100})/){
    print "Hi_A\n";
    $SPROC = $1; 
  }
  elsif ($_ =~ /^\*(.{36})\;(\d{1,5})\;(\d{1,5})\;([a-z|A-Z|0-9|_]{1,5
+0})\;(.{1,100})/){
    print "$_\n";
    push (@VARIABLE, $Variable);
    push (@CHOICE, $Choice);
    print "Hi_B\n";
    $unique = $1;
    $Component_number = $2;
    $elements_in_array = $3;
    $Variable = $4;
    $Choice = $5;
  }
  
    if ($_ =~ /^\sEND/){
      
      print "Hi_E\n";
      push (@VARIABLE, $Variable);
      push (@CHOICE, $Choice);
      

      $Command = join(' ', 
                'EXEC', 
                 $SPROC, 
                 join(', ', 
                         @CHOICE[1 .. $elements_in_array])) . ';';

      my $Request_id = $CHOICE[26];

      print "$Command\n";
      Got_Command($Command, $Request_id);

      undef @CHOICE;
      my @CHOICE;
    }
}

close FLAT_FILE;

my $source = $flat_file; 
my $dest = 'Bin'; 

move($source, $dest) or die "Error moving file: $!\n";

sub Got_Command  {
  my($Command,$Request_id) = @_;
  my $output_file = "Output/Output_file_".$Request_id.".txt";
  open (OUTPUT_FILE, "+>>$output_file");
    
    print "$Command\n";
  
  my $sthB_A =  $dbh->prepare($Command) or die "Couldn't prepare query
+: ".$dbh->errstr;
  
  $sthB_A->execute() or die "Couldn't execute query: ".$sthB_A->errstr
+;
    
  my $Return_results = "Select * from Result_storage_keep where Unique
+_identifier = ".$Request_id."\;";

  print "$Return_results\n";
  my $sth = $dbh->prepare($Return_results) or die "Couldn't prepare qu
+ery: ".$dbh->errstr;
  
  $sth->execute() or die "Couldn't execute query: ".$sth->errstr;
  
  while (my @row = $sth->fetchrow_array ) {
    print OUTPUT_FILE join("\t", @row); 
    print OUTPUT_FILE "\n";
  }
}
[download]

Few things.
1. Why capture $unique and $componen_number, since you aren't using them anywhere?
2. You don't need $elements_in_array, $#array will give the last elements number.

$elements_in_array = scalar(@array);
$last_element_index = $#array;
$last_element = $array[$#array];
# $#array is one less than the number of elements in array
# as first index in array is 0
# this is always true
if (scalar(@array) == $#array + 1) {};
[download]

3. Push things to your arrays immeadiately, instead of waiting for the next row. It makes it easier to follow whats happening later (at least I think so :)).