public static void zip(InputStream inputStream, String entryName, ZipOutputStream outputStream) throws IOException {
        outputStream.putNextEntry(new ZipEntry(entryName));
        int bufferLength = 1024 * 1024;
        byte[] buffer = new byte[bufferLength];
        int readed = inputStream.read(buffer, 0, bufferLength);
        while (readed != -1) {
            outputStream.write(buffer, 0, readed);
            readed = inputStream.read(buffer, 0, bufferLength);
        }
        outputStream.flush();
    }
...
OutputStream outresp = response.getOutputStream();
ZipOutputStream opzStream = new ZipOutputStream(outresp );
InputStream  istmp = new ByteArrayInputStream(out.toByteArray());
zip(istmp, "тут произвольное имя пишу", opzStream);