es6.js

self.onfetch = event => {
  const bodyStream = new TransformStream();

  event.respondWith(new Response(bodyStream, {
    headers: {'Content-Type': 'text/html'}
  }));

  [
    caches.match('/header'),
    fetch('/body'),
    caches.match('/footer')
  ].reduce((chain, responsePromise) => {
    return chain
      .then(_ => responsePromise)
      .then(r => r.body.pipeTo(bodyStream, { preventClose: true }))
  }, Promise.resolve()).then(_ => bodyStream.close());
};

es7.js

self.onfetch = async event => {
  const bodyStream = new TransformStream();

  event.respondWith(new Response(bodyStream, {
    headers: {'Content-Type': 'text/html'}
  }));

  const responsePromises = [
    caches.match('/header'),
    fetch('/body'),
    caches.match('/footer')
  ];

  for (let responsePromise of responsePromises) {
    const body = (await responsePromise).body;
    await body.pipeTo(bodyStream, { preventClose: true });
  }

  bodyStream.close();
};