The example in README seems to imply that simply doing z.write('/path/to/files/') is sufficient but that generates empty archives. Something like:
z = zipstream.ZipFile(mode='w', compression=zipstream.ZIP_DEFLATED)
for root, dirs, files in os.walk(path):
for filename in files:
file_path = os.path.join(root, filename)
arcpath = os.path.join(path, os.path.relpath(file_path, path))
z.write(file_path, arcpath)