Flash brackets are designed to get the flash up off the lens further, but many of them are also designed to keep the flash directly about the lens even in portrait orientation (verticles). This helps throw the shadow directly behind the subject and therefore eliminating, or at least minimizing the shadow.
Of course, as mentioned, having the main light source coming from the same direction as the camera is rarely ideal/flattering. So lighting a subject off-axis is better, but now you are dealing with shadows again. So there are some things you can do about it depending on your gear and location. If you have one off camera flash the closer you can get it to the subject and the larger you can make it the softer the light will be. Softer light means softer shadows. You can make a light source appear bigger by bouncing it off something, wall, ceiling, foam core board, reflector, umbrella, softbox, etc. The other tool to combat harsh shadows is to either add another less powerful light source on the side the main light source is going to cast shadows and fill those shadows with this weaker light to soften them. Another thing you can do is use a reflector on the shadow side to reflect some of the main light back into the shadows.