I figured it out, after poking around the WS class for a while. Here's what I did.
public class MailHelper {
public static Promise<WS.Response> send(EmailData emailData) {
WSRequestHolder mailGun = WS.url("https://api.mailgun.net/v2/feedmerang.com/messages");
mailGun.setAuth("api", "MAILGUN_API_KEY");
mailGun.setContentType(MediaType.APPLICATION_FORM_URLENCODED);
mailGun.setQueryParameter("from", emailData.from);
mailGun.setQueryParameter("to", emailData.to);
mailGun.setQueryParameter("subject", emailData.subject);
mailGun.setQueryParameter("html", emailData.body);
return mailGun.post("Sending Email");
}
}