Science-based: A flying creature cannot carry 200 lbs on its back, so determining how much food such a creature needs is impossible.
The world record for largest lift weight by a flying creature is a bald eagle that lifted a 15 lbs mule deer. Alaskan bald eagles (such as this one) have been known to weigh more than 17 lbs. There's no note as to how far this particular eagle was able to lift this particular mule deer, but it's likely not far. Generally, eagles are considered able to fly normally while lifting half their body weight.
Say we're generous, and eagles can fly normally with 3/4 of their body weight. That means a 17 lbs eagle can fly normally with a 12.75 lbs animal in its claws. Or, in other words, a 17 lbs eagle can lift about 30 lbs in the air (its own weight plus the weight of the animal it's carrying).
Let's now talk about the largest known flying animal, the quetzalcoatlus, which probably weighed around 500 lbs (if we're feeling generous; other estimates place its weight around 150 lbs). Now, you may think we're golden, because 3/4 of 500 lbs is 375 lbs. But, we have to take into account the square-cube law. Simply put, the square-cube law states that while area of something (for instance, wing surface area) increases at a squared rate, the mass will increase at a cubed weight.
Bird lift generation is directly proportional to the surface area of the wing. The wing chord of a large bald eagle is 27.2 inches. The wingspan is 90 inches. Let's be extra generous and say that the entire bird counts as wing, and the entire wing is the width of the chord. That gives our bald eagle 2448 square inches of wing (17 square feet). So, 17 square feet of wing can lift 30 lbs into flight. Hold that number.
Quetzalcoatlus had a wing span of 36 feet and a wing chord of about 4 feet. Using our same generous estimates, quetzalcoatlus had a wing surface area of 144 square feet. Quetzalcoatlus' wing surface area is 8.5 times the wing surface area of the bald eagle. 8.5 * 30 = 255 lbs. Our back of the napkin math states that quetzalcoatlus can't even fly its own weight if we use the largest weight estimates quetzalcoatlus.
But, maybe that's because our wing estimates are double what they should be (bird wings are more like triangles than rectangles). Let's run the numbers again, but with bald eagles having 8.5 square feet of wing and quetzalcoatlus having 72 square feet of wing. This makes quetzalcoatlus' wing surface area 8.5 times the wing surface area of the bald eagle... which is exactly the same number we got before. The important point here is that the relationship between the two needs to be correct, not that the exact numbers are correct.
We can see the same thing happen with land-bound animals that scale up: an ant can lift many times its body weight, a human cannot. An elephant that jumps down from a chair will break its own legs. Similarly, a shrike is said to be able to lift much more than its own weight, while a bald eagle can't even lift its own weight. Extrapolating out to a size that could carry itself plus 200 pounds, such a creature cannot exist on a planet with Earth gravity and atmosphere.
The other major problem with this scenario is the phrase "on its back". I want you to flap your arms and pay special attention to your back muscles. Now imagine doing the same thing in midair with 150 lbs strapped to your spine. To be able to fly, creatures need unrestricted range of motion for their shoulders and back muscles. The only way to strap something to the back of a flying creature is to strap something that's so small the creature barely notices it. In our case, that would mean something many, many times the size of the largest ever flying animal.
But, even if you put people in a basket the wyvern carried in its feet, it would still never get off the ground (as illustrated above).
See this answer to a meta question. This question is based on false premises (a flying creature that could carry 200 lbs on its back in a
science-based world). From the
science-based tag description: "For questions that require answers based on hard science, not magic or pseudo-science, but do not require scientific citations." (emphasis mine)