https://chromium-review.googlesource.com/c/chromium/src/+/1233613
This is a proposed solution.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/185ec6285ddeb538ecda4f0e057a406a226b524f

commit 185ec6285ddeb538ecda4f0e057a406a226b524f
Author: Maria Tarasova <marytarasova@yandex-team.ru>
Date: Tue Sep 25 17:33:23 2018

Fix data race in browsing_data_remover_test_util

If browser_tests is built with tsan enabled, Thread Sanitizer reports
data races in browsing_data_remover_test_util.

There are two threads to concurrently access the shared data, the
test’s main thread and a thread controlled by TaskScheduler singleton.
Both access browsing_data_remover_done_ and/or
flush_for_testing_complete_ fields to break run loop and exit test
after some cleanup occurs. In TaskScheduler’s thread, the write access
is done by the lambda function.

The proposed solution is to use the lambda call only to report the
asynchronous event to main thread, which becomes the only one to
access the fields implementing run loop break logic.

R=sky@chromium.org

Bug:  885188 
Change-Id: I706edb24ed362444cf46e558b1d54389179884da
Reviewed-on: https://chromium-review.googlesource.com/1233613
Reviewed-by: Robert Liao <robliao@chromium.org>
Reviewed-by: Scott Violet <sky@chromium.org>
Commit-Queue: Robert Liao <robliao@chromium.org>
Cr-Commit-Position: refs/heads/master@{#593987}
[modify] https://crrev.com/185ec6285ddeb538ecda4f0e057a406a226b524f/content/public/test/browsing_data_remover_test_util.cc
[modify] https://crrev.com/185ec6285ddeb538ecda4f0e057a406a226b524f/content/public/test/browsing_data_remover_test_util.h