Some non-issue stuff for a start. First, always use strictures (use strict; use warnings;). In this case you might discover that the chomps are chomping on $_ and not the loop variables I suspect you think they are chomping on. However you would be much better to chomp the whole slurped array rather than performing @input_data + @input_data² chomps:

chomp @input_data;
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There seems to be a missing ++$record_count; (I assume following the outer loop print).

Some advantage can be gained by pre-splitting the lines. Consider:

use strict;
use warnings;
use Benchmark qw(cmpthese);

my @data = <DATA>;

cmpthese (-1,
    {
    original => sub {original (@data)},
    presplit => sub {presplit (@data)},
    });

sub original {
    my @input_data = @_;

    my $record_count = 0;
    
    # Loop through the array
    for my $element (@input_data) {
    
       chomp $element;
       my @first = split(",", $element ) ;
    
       my $jcount = 0;
       my @result;
       # Loop through the array again
    
       for my $inside_elem (@input_data) {
            chomp $inside_elem;
    
            my @second = split(",", $inside_elem) ;
    
            # Build only elements below the diagonal
            last if ( $jcount++ > $record_count  ) ;
    
    
            # Covariance logic
            # No issues with the logic
            # sum of products of corresponding elements in the arrays
            my $sum = 0;
            my $count = 0;
            for (@first) {
                $sum += $_ * $second[$count++] ;
            }
            $sum /= scalar(@first) ;
    
            push @result, $sum ;
        }
       
        my $str_to_write =  join(", ", @result)."\n"  ;
        undef @result ;
    
        # Open the output file handler in append mode.
        #print $str_to_write;
        ++$record_count;
    }
}


sub presplit {
    my @input_data = @_;
    my $record_count = 0;
    
    chomp @input_data;
    @input_data = map {[split ',']} @input_data;
    
    # Loop through the array
    for my $first (@input_data) {
       my $jcount = 0;
       my @result;
    
       # Loop through the array again
       for my $second (@input_data) {
            # Build only elements below the diagonal
            last if $jcount++ > $record_count;
    
            # Covariance logic
            # No issues with the logic
            # sum of products of corresponding elements in the arrays
            my $sum = 0;
            my $count = 0;

            $sum += $_ * $second->[$count++] for @$first;
            $sum /= scalar @$first;
            push @result, $sum ;
        }
       
        my $str_to_write =  join(", ", @result)."\n"  ;
    
        # Open the output file handler in append mode.
        #print $str_to_write;
        ++$record_count;
    }
}

__DATA__
0.2939383839, -0.0929288282, 0.2939383839, -0.0929288282, -0.092928828
+2, 0.2939383839, -0.0929288282
0.0139383839, -0.1929288282, 0.0139383839, -0.1929288282, -0.192928828
+2, 0.0139383839, -0.1929288282
0.2009383839,  0.0929288282, 0.2009383839,  0.0929288282,  0.092928828
+2, 0.2009383839,  0.0929288282
0.0939383839,  0.5929288282, 0.0939383839,  0.5929288282,  0.592928828
+2, 0.0939383839,  0.5929288282
0.2939383839, -0.0929288282, 0.2939383839, -0.0929288282, -0.092928828
+2, 0.2939383839, -0.0929288282
0.0139383839, -0.1929288282, 0.0139383839, -0.1929288282, -0.192928828
+2, 0.0139383839, -0.1929288282
0.2009383839,  0.0929288282, 0.2009383839,  0.0929288282,  0.092928828
+2, 0.2009383839,  0.0929288282
0.0939383839,  0.5929288282, 0.0939383839,  0.5929288282,  0.592928828
+2, 0.0939383839,  0.5929288282
0.2939383839, -0.0929288282, 0.2939383839, -0.0929288282, -0.092928828
+2, 0.2939383839, -0.0929288282
0.0139383839, -0.1929288282, 0.0139383839, -0.1929288282, -0.192928828
+2, 0.0139383839, -0.1929288282
0.2009383839,  0.0929288282, 0.2009383839,  0.0929288282,  0.092928828
+2, 0.2009383839,  0.0929288282
0.0939383839,  0.5929288282, 0.0939383839,  0.5929288282,  0.592928828
+2, 0.0939383839,  0.5929288282
0.2939383839, -0.0929288282, 0.2939383839, -0.0929288282, -0.092928828
+2, 0.2939383839, -0.0929288282
0.0139383839, -0.1929288282, 0.0139383839, -0.1929288282, -0.192928828
+2, 0.0139383839, -0.1929288282
0.2009383839,  0.0929288282, 0.2009383839,  0.0929288282,  0.092928828
+2, 0.2009383839,  0.0929288282
0.0939383839,  0.5929288282, 0.0939383839,  0.5929288282,  0.592928828
+2, 0.0939383839,  0.5929288282
0.2939383839, -0.0929288282, 0.2939383839, -0.0929288282, -0.092928828
+2, 0.2939383839, -0.0929288282
[download]

Prints:

          Rate original presplit
original 205/s       --     -59%
presplit 498/s     143%       --
[download]