The largest flying creatures were pterosaurs. They, in turn, are reptiles or tetrapods, which makes them similar to dinosaurs and their modern representatives: crocodiles, lizards, and snakes.
Current understanding has pterosaurs as avemetatarsalians, just like dinosaurs and birds, and unlike crocodiles, lizards, and snakes.
Now, birds can be tough. The prime example is the conflict between the Australian Army (including the Royal Australian Artillery) and 20,000 emus known as the Great Emu War. The outcome was a decisive Emu victory.
Some people argue that this was not a conflict as it is frivolous to consider Emus as a military force.
However the fact they were capable of the formidable achievement of defeating a regular army proves they can, and this is also not the first conflict involving animals (e.g: https://en.wikipedia.org/wiki/Gombe_Chimpanzee_War).
Slightly off-topic, but I imagine there must be a world with balloon-like leviathans serenely floating through the sky like our airships, hosting mini-ecosystems on their bodies and under their shadows..
I mean, flying things that large aren't a physical impossibility; look at our airships from even 100 years ago.
Living things being that large isn't a biological impossibility either; look at whales or dinosaurs.
It just needs enough luck for enough variables to fall in place – and a lack of predators to pick on such a large and slow target – to support the evolution of such a creature. I suspect gas giant planets would have a higher likelihood of such lifeforms.
(Personally I just wish our terrestrial skies could be filled with such majestic sights; just look at real-world photographs of large airships flying low over rolling fields..)
Culture novels have Dirigible Behemothaurs and the The Algebraist has Dwellers. Two big floating lifeforms. Dirigibles live in airspaces and Dwellers in gas giants.
Current understanding has pterosaurs as avemetatarsalians, just like dinosaurs and birds, and unlike crocodiles, lizards, and snakes.