What is different or happens differently in winged creatures who fly that would preserve itself as evidence of their flying ability?
Most of the evidence for this would be determined by physics. Thanks to Newton and Bernoulli et al., we know the basic requirements for powered flight. So, if an organism exhibits the proper requirements i.e. large enough wings, proper musculature, etc. for flight, then it probably did fly. All of the modern flightless birds have evolved from birds with the ability to fly. As a result, they still have their wings, but they are reduced and/or modified. So, if you gave an animal flight expert the physical dimensions of an ostrich: the size and shape of it's wings, the density and size of the bones, etc. they would most likely accurately determine that an ostrich can not fly. Now obviously, for long extinct organisms, with only the fossil record to go from, determining flight is not always as clear cut. But, based on these parameters, one can get a good idea of whether or not an organism could fly. In a similar vein, if you gave a scientist the dimensions of an ostrich's long, dense, sturdy legs, they would probably determine that an ostrich does not do much gliding either, but gets around be walking and running, because creatures with those features usually do just that.
"There are three kinds of lies: lies, damned lies, and statistics."
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