How to get all the checked out files in a library with rest

Late to the party, but hope it can help someone. If you want to look up files with no previous check in versions (which are displayed in the ManageCheckedOutFiles.aspx page), you can use REST API and GetCheckedOutFiles().

https://contoso.sharepoint.com/sites/sitename/_api/web/lists/GetByTitle('ListTitle')/GetCheckedOutFiles()
It works at least in SharePoint Online. It will return only files with no check in versions, but not regular checked out files.