The standard Mail app from Apple does currently support e.g. iCould Drive, Dropbox, Google Drive, Documents 5 and OneDrive to grab attachments.
Other apps like Spark and CloudMagic also offer support for e.g. Box but not with e.g. Documents 5 if you start with their app to write an e-mail and attach the file. When you would open Documents 5 it's ofcourse possible to use your favorite e-mail app. I know only a select few apps that really attach the file itself and do not supply a link in the e-mail to the file which are Spark, CloudMagic, Boxer and Apple's own Mail app.
Check out
this topic which i started in September which offers quite a few apps that support attaching files to e-mail. I love
Spark on my iPhone and i use
CloudMagic on my iPad (since Spark is not yet available on iPad yet).
The standard mail app from Apple does have a very slow
way (press in e-mail message > press twice on '>' press 'add attachment' > select storage > attach a single file) of attaching files (per file) since iOS9. With Spark i can even attach multiple files at once from various source. Is Spark perfect would you ask? No but it comes close. See also the other topic i mentioned for my remarks on all these apps.