https://chromium-review.googlesource.com/c/chromium/src/+/1070649 will hook up clearing the DNS cache in the network service to chrome, but it lacks integration tests.

In particular, we should make sure closing an incognito window clears the cache, the browsing data remover correctly clears the cache, and gaia_screen_handler.cc clears the cache.  I'm going to restrict this bug to the first two, since I'm unfamiliar with the ChromeOS login screen.

We should have these tests before we ship the network service to stable, at least.