Should my aftermarket frame have a serial number on it?
I would be surprised if any quality frame does not have a serial number. Many manufacturers warn against frames with no number, or numbers scratched off, so your concern is somewhat valid and you should follow up on it. Also reading http://fbmbmx.com/products/frames/fbm_warranty.php suggests the frame should have come with a warranty card. 

Photograph the frame with the receipt and send it to them, specifically expressing your concerns. They will confirm fairly quickly if its genuine.