Support for gzip compression is already built into the phone through the zlib(3) library, your app can download a gzipped file and use the zlib library to decompress it. I'm not sure it there's support for ordinary zip files though.
But you should also keep in mind that when you access a file through the web, the web server usually compresses the file on the fly and the client decompresses it. So you might not need to do the compression/decompression yourself.