Maybe unnecessary?

docker_image_children.pl

#!/usr/bin/env perl

use strict;
use warnings;

my $input_image_id = $ARGV[0];
my $input_image_sha = `docker inspect ${input_image_id} --format='{{.Id}}'`;

exit if ( $? != 0 );
chomp $input_image_sha;

my $image_ids = `docker images -aq`;
my @image_ids = split "\n", $image_ids;
my %images;

for (my $i = 0; $i < @image_ids; $i++) {
  my $image_id = $image_ids[$i];
  chomp(my $image_data = `docker inspect ${image_id} --format='{{.Id}} {{.Parent}}'`);
  my @image_data = split " ", $image_data;

  # [ ID (SHA) => PARENT (SHA), ... ]
  $images{$image_data[0]} = $image_data[1];
}

my $current_sha = $input_image_sha;
my @shas = (
  $current_sha
);

for( ; ; ) {
  my $parent = $images{$current_sha};
  last if (! defined $parent);
  push @shas, $parent;
  $current_sha = $parent;
}

print join "\n", @shas;