Since Tuleap 10.8 a new REST route has been introduced allowing to retrieve information about a docman item (see story #12443
for more information). For items of file type, a "html_url" property is available in the representation allowing to download the file itself.
Unfortunately this link does not work does not work when the user is authenticated via a "pure" REST authentication methods (e.g. an access key) which can block quite a lot of useful integration.