Try to flush DOMStorage too when ending the browsing session.

content/public/browser/storage_partition.h

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #ifndef CONTENT_PUBLIC_BROWSER_STORAGE_PARTITION_H_
 #define CONTENT_PUBLIC_BROWSER_STORAGE_PARTITION_H_
 
 #include <stdint.h>
 
 #include <string>
+#include <vector>
 
 #include "base/callback_forward.h"
 #include "base/files/file_path.h"
 #include "base/time/time.h"
 #include "content/common/content_export.h"
 #include "net/cookies/cookie_store.h"
 
 class GURL;
 
 namespace base {
+class SequencedTaskRunner;
 class Time;
 }
 
 namespace storage {
 class FileSystemContext;
 }
 
 namespace net {
 class URLRequestContextGetter;
 }
@@ skipping 133 matching lines @@
   // Clears the HTTP and media caches associated with this StoragePartition's
   // request contexts. If |begin| and |end| are not null, only entries with
   // timestamps inbetween are deleted. If |url_matcher| is not null, only
   // entries with matching URLs are deleted.
   virtual void ClearHttpAndMediaCaches(
       const base::Time begin,
       const base::Time end,
       const base::Callback<bool(const GURL&)>& url_matcher,
       const base::Closure& callback) = 0;
 
-  // Write any unwritten data to disk.
+  // Write any unwritten data to disk, returns a collection of task runners
+  // that have been tasked with writing data.
   // Note: this method does not sync the data - it only ensures that any
   // unwritten data has been written out to the filesystem.
-  virtual void Flush() = 0;
+  virtual std::vector<scoped_refptr<base::SequencedTaskRunner>> Flush() = 0;
 
   // Clear the bluetooth allowed devices map. For test use only.
   virtual void ClearBluetoothAllowedDevicesMapForTesting() = 0;
 
  protected:
   virtual ~StoragePartition() {}
 };
 
 }  // namespace content
 
 #endif  // CONTENT_PUBLIC_BROWSER_STORAGE_PARTITION_H_