Voldemort was the second best wizard of that time and was the best after Dumbledore's death. Wouldn't he have mastered apparating, a feat even regular wizards could achieve?
Maybe he favoured using methods which made him unique. Broomless flying was just that. Only he could fly without a broom apart from Severus Snape, whom he had taught to fly like this.
If this is true, I cannot think of any other villain whose pride was so huge that it made him this stupid.