Typically search functionality doesn’t work on a list view with a microflow data source.
These forum posts outline how you can create a wrapper entity and associate the data to that entity and use the association to the wrapper entity as your data source. This allows for default search capability to be used:
Another approach you could take is to use the newer gallery widget as it will allow you to search on a microflow data source and is similar to a listview.
Hope this helps,