Is it true that hearing the sound of the flute distracted the Prophet, may Allah bless him and grant him peace, from his prayer, and thus his reward was magnified?

There is no Hadith (definition) indicating that not hearing the adhan (definition) (call to prayer) causes one to hear the sounds of musical instruments. However, there are authentic ahadith that indicate not hearing the sound of musical instruments like the mizmar (flute or wind instrument). For example, the Hadith of Ibn Umar, may Allah be pleased with them both: "He was with his servant Nafi’ – and Nafi’ was young at the time – and Ibn Umar heard a mizmar. He said: So he put his fingers in his ears and moved away from the road, and said to me: 'O Nafi’, do you hear anything?' I said: 'No.' He said: So he removed his fingers from his ears, and said: 'I was with the Prophet, peace and blessings of Allah be upon him, and he heard something similar and did something similar.'" We advise piety towards Allah and diligence in raising children to obey Allah and His Messenger, peace and blessings of Allah be upon him, especially in lands of disbelief where the dangers to young ones increase.