A rainbow is a phenomenon in which a white light ray (usually from a sun) reflects and refracts off particles in the air (in this case water particles from rain) to produce a spectrum of colours (due to the refractive index differentiation in colours). However, the length of a rainbow depends on how many particles there are for light to refract off, the angle in which it reaches the eye, and any objects that obscure the view of the rainbow. So, the largest rainbow could be found at a certain height above the ground (where no objects can obscure the persons view), where the particles in the air are prominent enough to form a full rainbow but not enough to obscure the view of the rainbow by dispersion of light via reflection off other particles. So in terms of how big a rainbow can be, it depends on the variables that act upon it, but unfortunately a rainbow cannot be accurately measured because it is a phenomenon of light particles, and not a physical object.