If I understand well you are looking for a way to make a query to your database and select only specific documents where the uid field matches the current user’s one.
In the cloud_firestore package documentation, assuming you are using this package, there is an example code which could be adapted to your requirement.
Let’s say you have a userId variable holding the current users’s uid in your flutter client code, then you could print all the description of that user’s documents with the following query:
.where("uid", isEqualTo: userId)
data.documents.forEach((doc) => print(doc["description"])));