The tests appear to have become flaky this morning, as there were about a dozen green runs before that.
https://ci.chromium.org/buildbot/chromium.fyi/Linux%20Xenial/

timbrown can you take this?

Any update on this?  The tests are still failing.

I'm looking at it now.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/5a5c586e49b5916234677f2a2a51cff76b777016

commit 5a5c586e49b5916234677f2a2a51cff76b777016
Author: Tim Brown <timbrown@chromium.org>
Date: Thu Apr 19 06:07:42 2018

Update previews_browsertest to use best practices

Specifically, EmbeddedTestServer should be recreated for every test and
only started after the browser process. Also reinitialize
ScopedFeatureList with every test as per recommended in header file.

Bug:  831838 
Change-Id: I3e90d69b2d7708ca4abd73577972c97f119c1ab1
Reviewed-on: https://chromium-review.googlesource.com/1018109
Commit-Queue: Tim Brown <timbrown@chromium.org>
Reviewed-by: Ryan Sturm <ryansturm@chromium.org>
Cr-Commit-Position: refs/heads/master@{#551955}
[modify] https://crrev.com/5a5c586e49b5916234677f2a2a51cff76b777016/chrome/browser/previews/previews_browsertest.cc

The first run with the change is #422. It is looking much much more healthy now, however there have still been a couple of failures.

I'll leave it running longer while I try to work out what's happening with the remaining failures.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/c3ba695ae8f5dbbd96254a9846b7cbc8f4f27050

commit c3ba695ae8f5dbbd96254a9846b7cbc8f4f27050
Author: Tim Brown <timbrown@chromium.org>
Date: Fri Apr 27 00:17:27 2018

Disable flaky Previews tests on Linux

The tests were already disabled on Windows and Mac for being flaky (the
feature is only enabled on Android and the tests should still be running
there).

Bug:  831838 
Change-Id: I14f0a97785e01033f094e75765734d33bff9a988
Reviewed-on: https://chromium-review.googlesource.com/1029179
Reviewed-by: Doug Arnett <dougarnett@chromium.org>
Commit-Queue: Tim Brown <timbrown@chromium.org>
Cr-Commit-Position: refs/heads/master@{#554209}
[modify] https://crrev.com/c3ba695ae8f5dbbd96254a9846b7cbc8f4f27050/chrome/browser/previews/previews_browsertest.cc

Closing as the tests have now been disabled (the CL went in on run #580).

Coincidentally, there hadn't been a Previews test failure in over a day before that, but I'm not convinced that would have continued. We'd seen that before.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/1ce8e07c5f19b1e793e6d17d13a3f747f21b1cb6

commit 1ce8e07c5f19b1e793e6d17d13a3f747f21b1cb6
Author: John Budorick <jbudorick@chromium.org>
Date: Fri Apr 27 23:58:31 2018

Redisable PreviewsNoScriptBrowserTest.NoScriptPreviewsEnabled.

Accidentally reenabled while disabling tests on Linux.

TBR=dougarnett@chromium.org,timbrown@chromium.org

Bug:  831838 , 837822 
Change-Id: I6d0f126e73ff8eac0ed1b48c2eaa149a2be70e04
Reviewed-on: https://chromium-review.googlesource.com/1034014
Reviewed-by: John Budorick <jbudorick@chromium.org>
Commit-Queue: John Budorick <jbudorick@chromium.org>
Cr-Commit-Position: refs/heads/master@{#554568}
[modify] https://crrev.com/1ce8e07c5f19b1e793e6d17d13a3f747f21b1cb6/chrome/browser/previews/previews_browsertest.cc

[timbrown]:  Disabling a test because it is flaky (And never telling the owners about it!) is not fixing the flaky test.  Please tell the test owners when disabling a test, and don't mark the bug about the test being flaky a fixed.

ACK.

Sorry about that. I thought putting dougarnett@ as a reviewer of the CL was sufficient notice. I closed the bug because AFAIU the feature/tests are not needed/run on Linux, and if I remember correctly, I found similar bugs about flakes on Mac and Windows which were similarly closed as the feature is not used on those platforms. I should have confirmed that with the owners though.

I'm sorry, I didn't recognize dougarnett as an owner when I came across this.  I still think it's better to leave bugs open, and add the label, to make sure all relevant parties are CCed.

Note that browser_tests do not currently run on Android (Issue 611756). Since some of the previews browsertests are currently enabled only on Android (https://cs.chromium.org/chromium/src/chrome/browser/previews/previews_browsertest.cc?rcl=be221fc5f10b2250a6bf6064cc51297b71f35656&l=147), this effectively means that those tests are not running on any platform.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/a875a2ea21d8a321295a11440c80af01bcf7fa86

commit a875a2ea21d8a321295a11440c80af01bcf7fa86
Author: Tarun Bansal <tbansal@chromium.org>
Date: Thu Jul 12 17:14:30 2018

Deflake resource loading hints and previews browsertest

Attempt to deflake resource loading hints and previews
browsertest by waiting for hints to be processed.

Currently, the hints are processed on the background thread,
and so may not be processed immediately.

Log from the failed Linux test bots seem to indicate that
the hints are not processed in time.
See http://shortn/_IjBGHDP2Rp

Bug:  789542 , 831838 
Change-Id: I6b30b1a86dc5d2cdef1cd8274cf5c6088bec8634
Reviewed-on: https://chromium-review.googlesource.com/1134598
Reviewed-by: Ryan Sturm <ryansturm@chromium.org>
Commit-Queue: Tarun Bansal <tbansal@chromium.org>
Cr-Commit-Position: refs/heads/master@{#574613}
[modify] https://crrev.com/a875a2ea21d8a321295a11440c80af01bcf7fa86/chrome/browser/previews/previews_browsertest.cc
[modify] https://crrev.com/a875a2ea21d8a321295a11440c80af01bcf7fa86/chrome/browser/previews/resource_loading_hints/resource_loading_hints_browsertest.cc

Have not seen any flake since c#14.