You can use this workaround to display product barcode on packing slips (without installing any apps). Edit your packing slip template (Settings > Shipping and Delivery > Edit Packing Slip Template) to replace the snippet that displays product SKU
{% if line_item.sku != blank %}
{{ line_item.sku }}
{% endif %}
with the following:
{% if line_item.sku != blank %}
{% for item in order.line_items %}
{% if item.sku == line_item.sku %}
{{ item.variant.barcode }}
{% break %}
{% endif %}
{% endfor %}
{% endif %}
Hope this helps