Try to flush DOMStorage too when ending the browsing session.

content/browser/dom_storage/dom_storage_context_wrapper.h

Index: content/browser/dom_storage/dom_storage_context_wrapper.h
diff --git a/content/browser/dom_storage/dom_storage_context_wrapper.h b/content/browser/dom_storage/dom_storage_context_wrapper.h
index 2c37e330b91a164044bea0da9f7dd3282880a5bd..9170791736a4dbcc4d6c835d035aadc3bef549d5 100644
--- a/content/browser/dom_storage/dom_storage_context_wrapper.h
+++ b/content/browser/dom_storage/dom_storage_context_wrapper.h
@@ -13,6 +13,7 @@
 #include "base/memory/memory_pressure_listener.h"
 #include "base/memory/ref_counted.h"
 #include "content/browser/dom_storage/dom_storage_context_impl.h"
+#include "content/browser/dom_storage/dom_storage_task_runner.h"
 #include "content/common/content_export.h"
 #include "content/common/storage_partition_service.mojom.h"
 #include "content/public/browser/dom_storage_context.h"
@@ -71,7 +72,11 @@ class CONTENT_EXPORT DOMStorageContextWrapper :
   // Called when the BrowserContext/Profile is going away.
   void Shutdown();
 
-  void Flush();
+  // 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.
+  std::vector<scoped_refptr<base::SequencedTaskRunner>> Flush();
 
   // See mojom::StoragePartitionService interface.
   void OpenLocalStorage(const url::Origin& origin,