The rules for Objects in the DMG, (pg 246), states this about Objects:
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book,table, chair, or stone, not a building or a vehicle that is composed of many other objects.
So, (to me), an Arcane Canon, a magical object, is already, somewhat, outside the normal definition of objects per the rules. An Arcane Canon, is most certainly animate.
The intent of the class, moreover, is for the player to describe what they are making. An origami paper dragon turret or even a turret made of brass, certainly are susceptible to burning or melting.
The Fireball spell says this:
The fire spreads around corners. It ignites flammable objects in the area that aren't being worn or carried.
So while creatures are allowed a saving throw, an object gets NO Saving Throw and is automatically subject to the effect, and catches on fire, (if appropriate), in addition.
Not being a creature, grants the Arcane Canon, less protection than a creature, not more.
To counter all rules lawyer-ish arguments the DMG states(pg 246):
Use common sense when determining a character's success at damaging an objects.
If the Jawas in Star Wars can shoot R2-D2 with a lightning gun, then it seems like common sense that someone could target a player’s, physical, Arcane Canon with a Lightning Bolt or a Fireball.
How the player choses to describe their Arcane Canon, is going to drive how it interacts with spells. Keep in mind, the Arcane Canon, as an object, is going to interact with spells, it has NO choice. It gets no chance to save itself.................not it is unaffected.