Im not sure it even has to be complicated and full on machine learning.
Could also just make it easy to share diagnosis to the a database stripped from personal information about the client, properly index it, share it worldwide, allow doctors to contact eachother automatically who match.
If it is a rare condition, reidentifying people from even small amounts of relevant data (age, gender, hospital visited) data is trivial. If it is a common condition, usually there is plenty of data already there.
Could also just make it easy to share diagnosis to the a database stripped from personal information about the client, properly index it, share it worldwide, allow doctors to contact eachother automatically who match.