whats the mimetype of the data you stored as file on parse?
Normally when you upload to parse you provide a file name to the parse api (including ".typ" ) that will indicate a mimetype to any subsequent GET requests. Those gets can just wrap http protocol with the parse remote data to have a single 'provider' type operation that simply consumes the data from parse in a single operation.
For example a media player can open/Play parse data directly when using a file Url like yours. If you store an mp4 on parse with a filename ending in ".mp4" you can simply open the Url to the parse file in a client app like VLC.
For you, you can just create a new HttpUrlConnection and read then data into an appropriate Object.
example where url is a parse.com FILE url like yours:
URL imageUrl = new URL(url);
HttpURLConnection conn = (HttpURLConnection)imageUrl.openConnection();
conn.setConnectTimeout(30000);
conn.setReadTimeout(30000);
conn.setInstanceFollowRedirects(true);
InputStream is=conn.getInputStream();
OutputStream os = new FileOutputStream(fileCache.getFile(url));
Utils.CopyStream(is, os);
os.close();