I found it to be fairly straightforward with plenty of resources available by googling parse-server and mailgun. If you don't need templatized emails then you can just add mailgun to your package.json and configure your mailgun adaptor in your index.js file like this:
new ParseServer({
databaseURI: xxx,
appId: xxx,
...
emailAdapter: {
module: 'parse-server-simple-mailgun-adapter',
options: {
fromAddress: 'donotreply@yourdomain.com',
domain: process.env.MAILGUN_DOMAIN,
apiKey: process.env.MAILGUN_API_KEY,
}
}
see also: https://stackoverflow.com/a/37757222/4228969