Light is an electromagnetic (EM) wave, and EM waves of all wavelengths (colours) have a constant speed of in vacuum.
Light through a medium have slightly lower speed and it is dependent on the refractive index of the medium.
The expression for the speed is , where, is the speed in the medium, is the speed in vacuum and is the refractive index of the medium.
The refractive index of the medium in turn in dependent on the wavelength of light as given by the expression, . Here, and are constants and is the wavelength of light.
A larger value of the wavelength will result in a lower value of the refractive index and in turn gives a higher value of the speed .
Hence, the speed of light in vacuum is same for all colors but red coloured light has the highest speed in a dielectric medium as it has the largest wavelength.