If your goal is to maximize your body’s ability to burn fat as a fuel, then Zone 2 is definitely the fat burning zone in which your body relies most heavily on fat as its primary source of energy. That being said, it doesn't necessary mean that by spending more time in Zone 2 you will increase that ability. There are other ways to burn fat effectively dependant on your requirements
ZONE 4 & ZONE 5
If you are trying to lose weight and burn off excess fat, then you actually need to train more in zone 4 and 5 in order to stimulate your fat burning metabolism. There is a myth out there that staying in the fat burning zone helps you to lose weight. Actually, it just makes sure that you don't burn carbohydrates as fuel and the intensity stays low. If you want to lose excess body fat, then you have to 'stoke' the fire so to speak and that means exercising very intensely. By exercising in Zone 4 and 5, then you burn off all your carbohydrates and then in the 4 hours after your workout, you burn a ton of fat as fuel. That's the key to really losing some excess weight.
If you want to burn fat in order to extend your endurance range in a racing situation, then I would offer a few different suggestions. Many pros that want to improve their ability to burn fat in races and therefore spare essential glycogen reserves for later in the race when they need them most. This means teaching your body to use fat first and foremost in every workout. One of the ways to do this is to start off every ride early in the morning before breakfast and ride for at least 2 hours before starting to feed. Ride at Zone 2 and 3 for those 2 hours and then your body is forced to burn fat. At the end of 2 hours, start eating some carbs and protein and then finish your ride with intensity and intervals. This will help to teach your body to burn fat at a higher level of exercise intensity, thereby sparing your carbohydrate stores for later.