It doesn't appear that Canada keeps much of a database
en.m.wikipedia.org
Originally, the program required the registration of all non-restricted firearms but this requirement was dropped on April 6, 2012, by the coming into force of Bill C-19.[2][3] Bill C-19 also mandated the destruction of the non-restricted records of the registry as soon as feasible.[4] The province of Quebec immediately filed a request for an injunction to prevent the destruction of the data. A temporary injunction was granted by the Superior Court of Quebec on April 5, 2012 to prevent the data for Quebec residents from being destroyed until legal arguments could be heard.[5] On March 27, 2015, the Supreme Court of Canada ruled in Quebec (AG) v Canada (AG) that the destruction of long-gun registry records was within the constitutional power of Parliament to make criminal law, denying the Government of Quebec's legal challenge and allowing for those records to be destroyed.
A Global News investigation into cross-border trafficking offers new insight on where Ontario's crime guns are coming and how they are being purchased.
globalnews.ca
The details from that seizure, and many others across the U.S., are vital to understanding how violence on Canadian streets unfolds.
Yet, there is no national database on the origins of Canada’s so-called crime guns, meaning there is still no broad view of where these firearms might be coming from.