If you find the interpolation or transition of the frames of your Custom Camera isn't smooth enough, you can change the interpolation to see if you can achieve better results. There are four options 1) Linear 2) FSLerp 3) SSLerp 4) LCurve. Each will transition between the frames in a slightly different manner to improve the movement of the camera as desired.

If you still cannot achieve the results necessary, consider using a Path camera for smoother movement.