Carrying arms under service to the nation places you under the National Defence Act, and there are provisions and exceptions there which apply to military members so as to allow us to carry/use/play with rifles, pistols, machine-guns, howitzers, AA Missiles, high explosives, etc, IN THE COURSE OF CONDUCTING OUR DUTIES AS MEMBERS OF THE CANADIAN FORCES.
As such, when you're on duty, the provisions of the firearms act do not apply.
When you're off duty, at home, etc, you would need to have a PAL in order to purchase a civilian firearm.
Note, there are special considerations for military members who own firearms and wish to live on base, ie you can't store them in your barracks room (among others) so use the search function, and read your base routine orders.
NS