I would just like to mention that one family of modern birds, Megapodidae, can also fly from birth.
What does this tell us about dragons? Did they fly at birth too?
Yes, they did. This is shown in that documentary about Danaerys Stormborn, the Unburnt, Mother of Dragons, Breaker of Chains, Khalisi of the Dothraki, Ruler of the Seven Kingdoms, and Queen of the Andals and the First Men.