I found this incendiary crossbow arrow of similare structure as the incendiary gun
The auction company compares the crossbow arrow with one at the Museum of history in Bern (germany). The arrow at this museum was found at the fortress of Altbüron (today's Switserland) which was destroyed in the year 1309.
This arrow at the museum gives us an even earlier date as to this design. Like Michael already stated though, the depiction of such a gunarrow with cannon first appeared in 1326-7
Auction: Hermann-Historica, 59 lot number 4609. qpril 9/10th 2010.