You can send files and other content to other apps from inside PrintDirect.

Tap on the 3 lined button in the top left of the screen to show the left side panel. Then tap on "Files" to show the file screen.

Tap on the checkbox in the file icon to select files and then tap on the action menu button (circle with 3 dots icon).
You can choose either the "Open with App..." or "Share" actions in the menu to share content with other apps such as Omnifocus, Devonthink, Evernote etc.

To save files to the Apple Files app, choose "Export" from the action menu and then choose Files App. Then you can choose where to save the file inside the Files app.