Thank you very much. I'll post the answer here so anybody searching can find the solution.
Add this to download URL:
{{ServerUrl}}/{{Platform}}/FileCabinets/{{FileCabinetId}}/Documents/{{DocumentId}}/FileDownload?targetFileType=zip&keepAnnotations=false
Be aware that clipped documents are already downloaded as a ZIP file. There is no double zip compression. You have to check if zip file contains one or more files.