You can use the datagrid extension widget to add an inline button to your datagrid that triggers a microflow.
In the microflow use the download activity to download your file. The microflow will have one parameter the same type as the data grid.
Depending on how your domain model is setup. The microflow will have one parameter the same type as the datagrid, then you can open a popup window (pass the object), and use the file manager widget to upload the file.
Here is the link to the datagrid extension widget (just a heads up that its not being supported anymore, but I've tested it in 7.11 and it works).
As an alternative, you could present your data using a Listview and style it like a datagrid. In a ListView, you can have buttons in each row. Using a Table or LayoutGrid enables you to present data in a grid like format using a ListView.