Instead of speculating about what might work, here's a threaded solution that does.

I've C&P's most of the code from your OP, but I've made various changes to adapt it to my environment. I only had one chromosome file kicking around ( Chr_22_14-09-2001 Release 3, [nucleotoides 13100001-47848585] ), so I used that multiple times. And for the motifes I just clipped out a few short (80 character) sequences at random.

The output goes to STDOUT. You could redirect this to a file via the command line or open STDOUT to a file before spawning the threads. On my system which has only 1 cpu, there is no conflict with writing to a file from multiple threads. Most threaded C-runtimes would serialise this for you, but if yours does not, it would only require the addition of 1 shared variable and two locks to do so.

The code creates a separate thread for each chromosome file in the list and passes the chromosome name as a paramater to each thread. Depending upon the number of chromosome files you are processing, it might be better to limit the number of concurrent threads--but given that each thread is also doing IO to the same file, it might be ok as is for upto 2 or 3 times the number of chromosomes as you have cpus. It will require a substantial amount of memory as written if the chromosome files are large, but with better knowledge of the task, the code can be easily adapted.

The motifs file is read and loaded into a shared hash and re-used by all the threads.

#! perl -slw
use strict;
use Carp;
use threads;
use threads::shared;

my $chr_file = $ARGV[0];
my $seq_file = $ARGV[1];

if ( 2 != scalar(@ARGV) ) {
    croak 'Invalid parameter number';
}
elsif ( ! -e $chr_file || ! -T $chr_file ) {
    croak 'Missing or invalid chromsome-listing file';
}
elsif ( ! -e $seq_file || ! -T $seq_file ) {
    croak 'Missing or invalid sequence-listing file';
}

my %motifs : shared;

sub thread {
    my $chromosome = shift;
    my $directory = 'fasta/';
    my $file = 'chr_'.$chromosome.'.fa';
    my $path = $directory.$file;

#    my $seqio = Bio::SeqIO->new(
#        -file    =>  "<$path",
#       -format  =>  'largefasta'
#    );
#   my $seq = $seqio->next_seq();
#    my $sequence = $seq->seq();

## Crude fasta load--Expects 1 sequence per file
    open my $fh, '<', $path or croak "$path : $!\n";
    <$fh>; ## discard header
    ( my $sequence = do{ local $/; <$fh> } ) =~ s[\s+][]g;
    close $fh;

    foreach my $motif ( keys(%motifs) ) {
        my $str = $motifs{$motif};
        my $len = length($str);
        my $pos = 0;

        while ( ($pos = index( $sequence, $str, $pos)) >= 0 ) {
            print join "\t", $chromosome, $pos, $motif;
            $pos += $len;
        }
    }
}

open my $fh_seq, '<', $seq_file
    or croak "Unable to open motif file: $seq_file";

while (<$fh_seq>) {
    s/^\s+//;
    s/\s+$//;
    my @row = split("\t");
    next if 2 != scalar @row;
    $motifs{ $row[0] } = $row[1];
}
close($fh_seq);


my @chromosomes;
open my $fh_chr, '<', $chr_file
    or croak "Unable to open chromsome list: $chr_file";

while (<$fh_chr>) {
    s/^\s+//;
    s/\s+$//;
    my $row = $_;
    next if !$row;
    push @chromosomes, $row;
}
close($fh_chr);

my @threads =  map{
    threads->new( \&thread, $_ )
} @chromosomes;

$_->join for @threads;

__END__
C:\test>568393 fasta\chromosomes.lst  fasta\motifs.lst
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6666540 6
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   6540    3
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   24666540        9
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   12666540        7
22_14-09-2001   540     2
22_14-09-2001   24666540        9
22_14-09-2001   540     2
22_14-09-2001   24666540        9
22_14-09-2001   24666540        9
22_14-09-2001   24666540        9
22_14-09-2001   540     2
22_14-09-2001   540     2
22_14-09-2001   24666540        9
22_14-09-2001   540     2
22_14-09-2001   24666540        9
22_14-09-2001   24666540        9
22_14-09-2001   540     2
22_14-09-2001   24666540        9
22_14-09-2001   24666540        9
22_14-09-2001   540     2
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It's easier to respond to questions if there are any than to try guess, and comment on what you might not understand.