I think you mean "dbMoveObject(Speed)", not Direction. And that will move the object in the direction it's pointing, not the direction the camera is pointing.
Generally things are done like this: The character moves around and the camera is then placed behind it. What you seem to want to do is the opposite.
In this case, you'd probably do something along the lines of:
dbPositionObject( obj, dbCameraPositionX(), dbCameraPositionY(), dbCameraPositionZ() );
dbRotateObject( obj, dbCameraAngleX(), dbCameraAngleY(), dbCameraAngleZ() );
dbMoveObject( obj, distance_from_camera );
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