I think these tests are actually really important to make sure that our first run flow doesn't break. Should this be a P1?

I looked at the second one (FirstRunTest.java), and it looks like it fails because of the "has first run already been shown" shared pref being set by a previous test :(.

Filed bug 908174 to address clearing shared prefs between tests, then we should be good to un-disable.

It sounds like clearing between tests is going take time, so as a short-term fix we should reset shared preference state.

There's another similar issue filed here in bug 911316

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/06acfc5326b0f0dac55b5993444d225e79060eb3

commit 06acfc5326b0f0dac55b5993444d225e79060eb3
Author: Yun Liu <yliuyliu@google.com>
Date: Mon Jan 14 20:15:13 2019

Clear app's SharedPreferences before each test to reduce flakiness.

It should fix FirstRun tests flakiness issue if FirstRun tests were
failed because shared pref being set by a previous test.

Bug: 908174, 902774
Change-Id: I9480750a60da1344a72e105ffc444dd982cb36b1
Reviewed-on: https://chromium-review.googlesource.com/c/1399542
Reviewed-by: John Budorick <jbudorick@chromium.org>
Reviewed-by: Boris Sazonov <bsazonov@chromium.org>
Commit-Queue: Yun Liu <yliuyliu@google.com>
Cr-Commit-Position: refs/heads/master@{#622569}
[modify] https://crrev.com/06acfc5326b0f0dac55b5993444d225e79060eb3/base/test/android/javatests/src/org/chromium/base/test/CommitSharedPreferencesTestRule.java

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/2c298c962528b108c5916a3f31d0ffb1936bb5cf

commit 2c298c962528b108c5916a3f31d0ffb1936bb5cf
Author: Yun Liu <yliuyliu@google.com>
Date: Wed Jan 16 00:42:38 2019

Re-enable FirstRunIntegration tests.

Re-enable these tests after change to clear SharedPreferences before each test.
Related cl: https://crrev.com/c/1399542

Change-Id: I4fba9c11cbf2168a924ca867965c92a9046ff36e
Bug: 908174, 902774
Reviewed-on: https://chromium-review.googlesource.com/c/1409821
Commit-Queue: Yun Liu <yliuyliu@google.com>
Reviewed-by: Boris Sazonov <bsazonov@chromium.org>
Reviewed-by: John Budorick <jbudorick@chromium.org>
Cr-Commit-Position: refs/heads/master@{#622941}
[modify] https://crrev.com/2c298c962528b108c5916a3f31d0ffb1936bb5cf/chrome/android/javatests/src/org/chromium/chrome/browser/firstrun/FirstRunIntegrationTest.java