No! The problem with your image is Red Eye, not Flare or Ghosting. That said, I Always use a lens hood and recommend that you do the same though it will not prevent red eye.
Red Eye is a result of the light projected by the flash reflecting from the back of the subjects eye back to the camera. Since your SB-400 has a very low profile the center line of the flash is very close to the centerline of the lens. This allows the light to go through the subjects pupils and reflect directly (180 degrees) back to the sensor. Using a telephoto lens makes the problem worse. Even an SB-900 ( which has a much higher profile) will produce red eye when using direct flash and a long lens. The best way to eliminate red eye is to turn up the ISO and not use flash. When using flash is the only option use bounce flash or use a flash bracket or hold the flash in your hand (with an SC-28 or SC-29 TTL extension cord) to get the flash unit high above the lens. The longer the focal length, the higher above the lens you must be. That way the light can not reflect directly back to the sensor. You can also try using Red Eye Reduction mode so the Speedlight fires a few pre flashes to close the subjects pupils which may or may not be effective. (I never use it). Getting closer and using a wider focal length would help also. Good Luck and Enjoy your Nikons!