I ran this past 2 senior mechanical design engineering from Honeywell who I worked with before I retired. They disagree. I copied exactly what was said and emailed it to them:

"Nope. I don't buy it at all.

It is true that that kinetic energy is 1/2mv^2.

You are not doubling the velocity simply because there are two projectiles, as is proposed down below, you are doubling the mass of the projectile (i.e. 2m), and both projectiles will be moving at the effectively the same velocity. So, the energy will be doubled."

and

"Conservation of energy. Each bullet has a specific, and in this case equal, amount of energy. The kinetic energy doubles from firing 2 bullets simultaneously. The kinetic energy of the gun in recoil doubles vs firing one bullet, so the velocity of the gun increases by the square root of 2 (1.414), not by 2.
Force acting on the rifle is equal to the force acting on the bullets and F=ma. Acceleration of each bullet is unchanged from firing each one separately or together, and each is equal. You have the mass of 2 bullets firing instead of one. So the force becomes F=ma+ma=2ma. So the force doubles and the recoil doubles.
Equivalently, force = change in momentum = mv/t. Here's another equation showing velocity. By firing 2 bullets simultaneously, F = mv/t + mv/t = 2mv/t. So the force doubles and the recoil doubles."