Small correction:

Galactic radius increases with time:

R = k * t

The correct substitution is this:

KE = 0.5 * m * (a * R / k)^2

Most materials and structures are held together by electromagnetic forces, e.g. a house. Galaxies are held together by gravitational forces. A force is a force. Therefore a galaxy is a structure. The area of the galaxy would act like a sail, the more area the more solar radiation / wind energy it would collect. Intergalactic radiation would transform directly to kinetic energy for the galaxy. Thus we may live on a galactic-sized radiation sail, getting bigger as time passes, and picking up speed, accelerating away from other galaxies at a constant rate.