I'm going to assume that the timestamp lines are unique and that duplicate blocks don't have to have the same timestamps.

#! /usr/bin/perl

use strict;
use warnings;

my ($key, %hash, @keys);
while (<DATA>) {
        if (/^\@:\d{10,}:(?:\d{10,})?:1$/) {
                chomp;
                $key = $_;
                # needed to process keys in file order
                push @keys, $key;
        } else {
                $hash{$key} .= $_;
        }
}

my ($value, %revhash);
# changed to foreach to process keys in file order
# while(($key, $value) = each %hash) {
foreach $key (@keys) {
        $value = $hash{$key};
        if(exists($revhash{$value})){
                print "$key is a duplicate of $revhash{$value}\n";
        } else {
                $revhash{$value} = $key;
        }
}

__DATA__
@:1107530184::1
kkkkkkkkkkkkmkmkmk
kkkkkk
confused.gif
@:1107530257:1107530439:1
kmkmkm
<br>kmkmkm
<br>
<br>Fri Feb  4 10:17:37 2005
<br>
mad.gif
@:1107530709::1
ygyg
ygygygyg
lol.gif
@:1107530717::1
ygyg
ygygygyg
lol.gif
@:1107530963::1
cool
help
cool.gif
@:1107532649:1107532689:1
k
<br>kkkkkkkkkkkkkkkkk
<br>
<br>Fri Feb  4 10:57:29 2005
<br>
lol
lol.gif
@:1107532758::1
lll
Lets
mad.gif
@:1107532976::1
lll
Lets
mad.gif
[download]

And the output is:

@:1107530717::1 is a duplicate of @:1107530709::1
@:1107532976::1 is a duplicate of @:1107532758::1
[download]

Update: If you only want to eliminate one block from each pair of consecutive duplicate blocks then this might work:

undef $/;
my $file = <DATA>;
$file =~ s/^\@:\d{10,}:(?:\d{10,})?:1\n(.*?)
          (^\@:\d{10,}:(?:\d{10,})?:1\n\1)/$2/msxg;
print $file;
[download]