Many of these children were conceived by parents who are no longer together. Many others are from parents who already have full families and are now grandparents or even great grandparents. Some parents passed away long ago. Whose children are they?
It could be possible to write this from the point of view of one of these snowflake children as they are in school or approaching adulthood. Teenage and college years are already full of crises of identity; this character would really be trying to understand who they are and what the idea of family means. It is possible that they have joined with other snowflake children as a means of unity. Perhaps they are viewed as second-class citizens.
One branching possibility is that while the controversies continue in the public eye, someone comes to the realization that a large number of these snowflake children are missing. On investigating, they discover that secret agencies have been taking and raising these children as part of black ops teams that are involved in national and corporate espionage (This idea may have been inspired by the upcoming Black Widow movie).