Big thanks to Sandy Ussia for her help with this post!
These steps will show you how to create a Flow that will move a selected document from one SharePoint library to another. If you want to move a document to a library in a different Office 365 tenant or SharePoint environment follow the same steps but make sure you change the SharePoint connection in the Copy File step.
For this solution you will need two SharePoint document libraries.
To get started navigate to the library that you want to move the document from.
Click on Create a flow from the Flow dropdown.
Click on more options then on Complete a custom action for the selected item.
Verify the SharePoint connection and then click on the Continue button. The flow will come with a For a selected item and Get item step. Nothing needs to be changed in these steps. Click on +New Step button then on Add an Action.
Search for SharePoint then select Get file properties. Select the Site address and Library name of the library you want to move the document from. Click on Dynamic Content and then select ID for the ID field.
Click on +New Step button then on Add an Action again. Search for SharePoint then select Get file metadata. Select the Site address. Click on Dynamic Content and then select Identifier for the File Identifier field.
Click on +New Step button then on Add an Action again. Search for SharePoint then select Copy File. Select the Site address for the library you want to move the document to. Click on Dynamic Content and then select Path for the Source File Path. For the Destination File Path field Type in /LibraryName/ then select Display Name from Dynamic content. The Overwrite Flag decides whether the file will overwrite a document with the same file name.
Click on Save Flow
To test the Flow navigate back to the original library and select an item. Click on the Flow dropdown and click on the name of the Flow you created. Click on Run Flow.