I’d like to create fantasy creatures that can fly using their own realistic physiology without magic or any kind of supernatural power. Many references on the internet mention that popular dragons like in GoT and LoTR are not realistically possible to fly given their anatomy and design. And in our earth history itself, flying dinosaurs or primordial birds is not big enough for my purpose of world building. So, how do I conceptualise a very large group of flying animals that are very plausible for them to fly on earth and being a mode of transportation for human race? Is there any good references for building a physically realistic creature?
Quetzalcoatlus may be the largest flying creature in Earth's history, with an 11m wingspan. If that's not big enough, take 10 of them and attach them together in a long train. You could have an animal like that, a sky-snake with many sets of wings.
You could have a gliding bird with a central body and wings like a 747. It would need to be very thin and light for its size. It would not be able to flap the wings much, and probably could not take off from the ground, but it could live its whole life in the air, catching thermals. It could have sets of smaller wings that it could flap for thrust. It might be able to land on very tall cliffs where it could use the drop to get airborne again.
You could have a giant winged blimp-bird filled with hydrogen, or with hot air heated by a special organ. Perhaps the top of it could be transparent so the interior can be heated by sunlight, like a greenhouse, though that alone would not be enough heat. There are few limits on the size of a blimp. They could be as big as a blimp. The only question is what blimpy would eat. Perhaps they could photosynthesize. Or their insides could serve as a roost for other birds, and when the other birds die naturally they fall to the bottom and the blimp digests them.
Very big (if you include lighter-than-air creatures)
Historically, airships were massive, dwarfing even the biggest flying machines we have today from rockets to aircraft to (the few) of today's airships. Interestingly, one of the major challenges in constructing these airships in the early 1900's was finding a material that's lightweight and gas proof. The answer? The engineers turned to nature and used the cow intestines for their gas-bags.
Now, we don't have any real-life examples of lighter-than-air flying creatures, but I think clearly it is within nature's biological toolbox to create gas-tight membrane, just like generating a lifting gas is also possible (there are some microorganisms and algae types that produce hydrogen), I don't see a reason why you couldn't have "whales of the sky" that use enormous gas-bladders to float and filter-feed insects or smaller flying creatures like whales do in the ocean.
Without magic or physics bending, and staying within the bounds of biology, using gas-based lift like this basically means that there is no upper limit from a lift-perspective (it actually gets more efficient at scale for square-cube reasons), however there would need to be an ecosystem to support these creatures and an appropriate evolutionary pathway that created them in the first place.
Is there any good references for building a physically realistic creature?
No, there is nothing you could scale up believably that would be reasonable for human transport unless it's very short flights. Powered flight is very expensive in terms of energy use. Gliding isn't but that doesn't seem to be what you're after.
So you could scale up a Haast Eagle or a Condor and get them to pick you up and take you a few km, but not fly around with you touring the countryside.
The biggest problem is the weight of the human and their gear. You're more than 4 times the weight of the heaviest flying birds (they're under 20kg) and evolution does not put that sort of redundancy into animals. They evolve for what they need, not what would be convenient for humans. Sometimes the two coincide, but not at that scale.
You might be able to train teams of large birds to pull a glider though.