tl;dr: If you've already hand-waved in a 12m long, massive, winged, fire-breathing, flying creature, armor really isn't much more of a stretch, so put whatever you want on them. Dragons are already so entrenched as a fantasy genre staple that nobody is looking too closely at weight ratios.
The reason dragons—or any other significantly sized, winged flying animals—don't exist has to do with size to strength and weight to wing surface area ratios and metabolic constraints. The real question is could a naked 12m long dragon fly at all, and, in the absence of magic or other hand-waving, the answer is absolutely not.
The first issue is that strength doesn't scale up as quickly as weight due to the cube-squared problem. A good discussion can be found here, which I found via this answer.
The gist is that muscle strength is proportional to the surface area of the cross-section of the muscle strand, a two-dimensional measurement, so strength will vary (roughly) with the square of size. Weight depends on the volume of the creature, a three-dimensional measurement, so weight will vary with the cube of size.
The result is that the highest strength to weight ratios are found at the smallest scales. An ant can lift and carry 50 times its own weight, I can lift and carry only 1/4 to 1/2 of my own weight, and the very largest dinosaurs could likely only barely lift their own body mass. (The very largest animals, whether modern or prehistoric, were aquatic, as they are too big to lift their own mass.)
Now, your dragons are 12m long (about 39 feet), which is about the length of a T-Rex. Depending on who you ask, tyrannosaurs weighed between 5.4 metric tons (6.0 short tons) and 6.8 metric tons (7.5 short tons). I wouldn't think it unreasonable to assume that a dragon of similar size would fit somewhere into that weight range, but that means we are dealing with an animal with the length and mass of a school bus. How could it fly if it can barely keep its body off the ground with its legs?
When the animal is winged, another limiting ratio comes into play at takeoff: mass to wing surface area. As discussed here, the wing surface area required to provide enough lift to get off the ground will grow much faster than body weight as a creature is scaled up. Small birds can get away with small wings. Bigger birds require a much larger wingspan for their mass.
Ruby-throated hummingbirds max out at 0.006kg weight and 0.11m wingspan.
American crows max out at 0.62kg weight and 1m wingspan.
Mallards max out at 1.58kg weight and .98m wingspan.
Peregrine falcons max out at 1.5kg weight and 1.2m wingspan.
Bald eagles max out at 6.3kg weight and 2.3m wingspan.
Wandering albatrosses, which have the largest wingspan of any living bird, max out at 12.7kg weight and 3.5m wingspan.
Of course, most dragons are depicted as featherless, with wings more like those of bats or pterosaurs than those of birds. This fact actually makes a flying, massive dragon even less workable, as bat's wings are very thin and fragile, composed of delicate skin stretched over bones with low mineral density (and thus high fragility). They rip and tear easily and would be even more prone to damage as you scale them up.
Here is a table with bird and bat wing loadings which shows that even the largest bats have a mass-to-wing-surface-area ratio lower than that of a hummingbird.
It turns out feathers are an efficient way of increasing wing surface area without adding much weight, but even feathers run into limitations; body mass in birds is actually constrained by how long it takes to replace flight feathers during molting.
So let's look at the quetzalcoatlus, very likely the largest creature to ever fly. A pterosaur, it massed over 200kg with a wingspan of up to 12m.
We're still not even sure how quetzalcoatlus got off the ground or whether they were even capable of more than long glides from a high starting point and relied on thermals to climb.
But, making the completely arbitrary assumption that a 12m long dragon masses at least in the ballpark of a similarly sized Tyrannosaurus Rex—let's just call it 5000kg—that is still 25 times the mass of quetzalcoatlus. What kind of wingspan would our dragon need to have?
This article attempted to (very roughly) predict the required wingspan of a human-sized (70kg) bird.
This article on wing loading says that the maximum for bird flight is 25kg body weight per square meter of wing surface area (Wikipedia backs it up). It also mentions that an elephant weighing 3.5 metric tons (which is actually small for an elephant according to Wikipedia) would need a wing surface area of 1750 square meters to take off. That's larger than six tennis courts, and basically requires the wings be made of aluminum or some other man-made material just to not buckle under their own weight. A dragon's wings would have to be prohibitively massive.
The final issue is metabolism. Dragons run into both the huge caloric requirements of dinosaurs (or any other multi-ton creature) and the even more demanding metabolic needs of flight. You don't get giant apex predators without giant prey (as with dinosaurs) or highly efficient feeding on concentrated food sources (like the way blue whales gorge on up to 3.6 metric tons of krill in a single day).
So where is your dragon getting his calories?
My brief research into metabolic requirements for flight determined that the topic is complicated. Really complicated. I'll come back to it when I have more time.
In conclusion, biology is all about tradeoffs, and dragons, envisioned as you describe, don't make any.
In earthlike gravity, air density, and physics, it's unlikely they could exist and fly at the scale you suggest even if designed expressly for that purpose. With or without armor.
On the other hand, we've identified dragons' only natural enemy: the square-cube problem!