Say in a post nuclear holocaust world, elephants managed to survive and adapt. It can consume and digest iron and steel and grow two rows of metallic tusks. When threatened the elephant will lift up iron rich rock and accelerate it by creating Lorentz force to impale the enemy at a distance up to 50m away. Similar to a certain species of fish (elephant nose), the elephant can generate its own electricity inside its body. Is this animal biologically possible?
Even with bones of steel, firing large supersonic projectiles would cause more kick than an elephant's tendons can withstand. His head would come off.
So I am not one to doubt the extraordinary products of evolution. They regularly surpass our wildest expectations. However, the forces involved in a railgun that can strike 40+km away are incredible. One of our issues with railguns is that, despite having some of the most advanced composites known to mankind, we still have a tendency of splitting the barrel lengthwise when we fire the gun.
Also note that the amount of energy required is unseen in the wild world. Perhaps Wikipedia puts it best:
Therefore, typical military railgun designs aim for muzzle velocities in the range of 2000–3500 m/s with muzzle energies of 5–50 MJ. For comparison, 50MJ is equivalent to the kinetic energy of a school bus weighing 5 metric tons, travelling at 509 km/h (316 mph).
The real trick, of course, is the fast discharge. 50MJ is roughly the amount of energy in a Snicker's bar, which is small peanuts for an elephant. However, it's also the amount of energy released by 1 kg of TNT! The TNT just releases it faster. It still doesn't release it as fast as a railgun needs it. Railgun discharges are just a few milliseconds long and need to pour all of the energy into the round in that time.
What would be the intermediate forms? A design like that doesn’t appear fully formed. It needs to be a gradual set of changes, every step of which is good for something on its own.
Even so, this would take millions of years. So it would not be a post-apocoliptic time frame, but an “epoch after man” time frame.
Evolution requires a reason (an evolutionary pressure) to evolve something. Not only must all of the issues discussed for an engineered elephant be overcome, but what possible use is a rail gun to a naturally evolved creature? It needs to eat, sleep, defend itself, and breed. All of those actions either don't need the force of a rail gun or are far more easily solved with something much, much simpler like tusks or teeth.
Suggesting that an elephant's opponent had natural armor necessitating the rail gun begs the question, "why the armor?" because one had to come before the other. In other words, there would never be a rail gun because the armor would never need to be that strong, there being no rail gun.
Said simply, no. Evolution would never produce a natural rail gun.
But could I engineer an elephant with a rail gun snout?
The answer is still no.
The magnetic strengths required to move even an object the size of a bullet exceed the electricity-storing and electricity-generating capacity of biology. It takes a substantial amount of power using the best conductive metals to move objects at speed.
Metal and biology don't go well together. Most metals in more than itty-bitty amounts are toxic to biology. Not using metal means dealing with the electrical resistance of the semi-conducting material. That's a deal-killer.
Newton's third law is also a deal killer here. For every action there is an equal and opposite reaction. The force required to fire the round demands massive magnetic fields and a substantial body structure to withstand the force. While wyldstallyns' answer is true at supersonic speeds, even if we reduce the muzzle velocity to that of a simple pistol (about 150 m/s), we're dealing with more force than can be achieved with the multiplying moment-arm of an arm, a baseball player can only hit about 100 miles-per-hour (45 m/s).
Nature doesn't like straight lines. Books have been written about how to detect man-made objects by looking for straight lines and 90-degree angles. However, without a straight line your hope of hitting your enemy with the round is zero. An elephant's trunk isn't straight and can't be made straight.
finally, biology is weak when it comes to rigid and strong. Even bones are flexible and can't bear a lot of force. The elephant's trunk needs to withstand the passing of a round at a minimum of pistol muzzle velocities (about 150 m/s). The bullet would rip through the trunk. If it was made of bone and perfectly straight, the heat and force of passing would break the bone apart. Remember that any air in the "muzzle" must be pushed out at whatever speed the round is subjected to.
Fantasy creatures like Kaiju are fun and there's nothing at all stopping an author from handing one a biological rail gun. But if you're looking for the plausibility of evolving or engineering such a thing — it can't be done.
You might have biologists tweaking elephant genes before the apocalypse, developing it as a weapon. But maybe a coil gun through the snout would work better than rails