The draw.io data in Confluence Cloud consists of two parts, the (1) macros in the pages that point to the (2) attachments on the pages that contain the diagram data (no data is held externally).
Both the macros and attachments will port as part of a standard Cloud->Server migration.
There is an additional step to migrations. Links in diagrams to Confluence pages contain the page ID of the page. Page names are not used since these break when a page is renamed. The migrated Confluence Server instance will change all of the page ID values.
We are in the process of implementing an export of the pageID mapping from Confluence Cloud and an import into Confluence Server. The export from Confluence Cloud is complete, so if you must migrate now, export the mapping and retain that mapping until the mapping importer is complete in Server (due Q3 2019).
You can find the exporter on your Confluence Cloud instance at https://xxxx.atlassian.net/wiki/plugins/servlet/ac/com.mxgraph.confluence.plugins.diagramly/drawioConfig, replacing xxxx with the appropriate base URL of your instance.
Click on the "Page IDs Export" tab.
Click "Start Export" and, when finished, the mapping will output to the text area below. Select it all, copy and paste it into a text editor and save.