I don't think so. 'Three Little Birds' seems to be more of a creative composition, perhaps aiming to bring joy or offer a message, rather than being tied to a true story.
Well, without more context, it's hard to say exactly. It could potentially be a story based on three birds that had some significance to a person or a community. Maybe they were seen as a symbol of hope or freedom, and the true story could revolve around how they came to represent that. For example, they might have shown up at a crucial time in someone's life and brought a sense of peace or inspiration.
It could be that they are teaching the younger birds in their group. By sharing these stories, they can pass on their knowledge and experiences, like how to find food in different seasons or how to avoid predators.