If your product line and serial number line are sibling records then you will need to use a custom Xslt and the xsl:key element.
However, an easier way may be to change the flat file schema.
Header record
Invoice A header record
Line
Product 1 for Invoice A record
Serial Number record for Product 1
Line
Product 2 for Invoice A record
Invoice B header record
Line
Product 3 for Invoice B record
Serial Number record for Product 3
i.e. create a Line record which has a child Product record and an optional Serial number record.
In the map connect the Line record to the Looping functoid to the output record.