One day one of this species is born/hatched with flaps similar to wings.
Individuals don't evolve, entire species do. Evolutionary events don't happen in "one day", they happen over many generations.
As for the evidence of the evolution of the winds, for birds we have quite a bit from the fossil record:
Notice how it doesn't go right from running to flying? There are many intermediate stages of jumping and gliding before you get from running to flight.
We can see some of the key features along the way in the fossilized bones that have been found:
Its also interesting to see that a lot of different animals, including those that do and do not fly, share the same bone types and locations. This is because evolution works by gradually modifying what is already present rather than introducing whole new plans like you seem to be suggesting:
The following image does a better job of detailing which bones are where and how they have changed over time, within just reptiles in this case (click to enlarge):
That came from here if you want to check it out:
Pterosaur Wings
Any questions so far?
Can you see that there is, in fact, evidence for the evolution of flight?