code.gs

function myFunction() {
  var body, channel, messages, threads, url;

  channel = '#general' // your slack channel
  url = 'https://hooks.slack.com/services/hoge/piyo'; // your slack incoming webhook url

  threads = GmailApp.search('is:unread');
  threads.map(function(t) {
    messages = t.getMessages();
    messages.forEach(function(message){
      if (message.isUnread()) {
        body = message.getSubject() + "\n\n" + message.getBody().replace(/<style.*?>[\s\S]*<\/style>/g, '').replace(/<br[^>]*>/g, '\n').replace(/<("[^"]*"|'[^']*'|[^'">])*>/g,'').replace(/\s{2,}/g, '\n') + "\n\nhttps://mail.google.com/mail/u/0/#inbox/" + message.getId();
        slack(body, channel, url);
        message.markRead();
      }
    });
  });

  function slack(message, channel, url) {
    var params, payload, response;
    payload = {
      'text' : message,
      // @ is ↓ change your slack account, remove comment out, and ↑ comment out
      // 'text' : '<@shy_azusa>: ' + message,
      'channel' : channel,
    };
    params = {
      'payload' : JSON.stringify(payload)
    };
    response = UrlFetchApp.fetch(url, params);
  }
}