Some of these failures appear to be related to https://bugs.chromium.org/p/chromium/issues/detail?id=750786, but a few of the OmniboxViewTests appear to be failing for a different reason. 

Failure stack trace:

[ RUN      ] OmniboxViewTest.CutTextToClipboard
Xlib:  extension "RANDR" missing on display ":99".
[29626:29626:0731/131224.635998:WARNING:password_store_factory.cc(255)] Using basic (unencrypted) store for password storage. See https://chromium.googlesource.com/chromium/src/+/master/docs/linux_password_storage.md for more information about password storage options.
[29626:29626:0731/131225.158799:FATAL:observer_list.h(276)] Check failed: false. Observers can only be added once!
#0 0x000002ce2517 base::debug::StackTrace::StackTrace()
#1 0x000002cfbce1 logging::LogMessage::~LogMessage()
#2 0x000000748b05 base::ObserverListBase<>::AddObserver()
#3 0x000003d5fcfc history::HistoryService::AddObserver()
#4 0x000000526a87 OmniboxViewTest::AddHistoryEntry()
#5 0x000000537806 OmniboxViewTest::SetupHistory()
#6 0x000000537267 OmniboxViewTest::SetupComponents()
#7 0x000000535a7d OmniboxViewTest::SetUpOnMainThread()
#8 0x0000024cdb1c content::BrowserTestBase::ProxyRunTestOnMainThreadLoop()
#9 0x00000239bcbd ChromeBrowserMainParts::PreMainMessageLoopRunImpl()
#10 0x00000239aa0a ChromeBrowserMainParts::PreMainMessageLoopRun()
#11 0x000000d7e40d content::BrowserMainLoop::PreMainMessageLoopRun()
#12 0x000001178e17 content::StartupTaskRunner::RunAllTasksNow()
#13 0x000000d7c64e content::BrowserMainLoop::CreateStartupTasks()
#14 0x000000d8138e content::BrowserMainRunnerImpl::Initialize()
#15 0x000000d79a02 content::BrowserMain()
#16 0x000002088dec content::RunNamedProcessTypeMain()
#17 0x000002089758 content::ContentMainRunnerImpl::Run()
#18 0x000003b39db6 service_manager::Main()
#19 0x000002088202 content::ContentMain()
#20 0x0000024cd7c7 content::BrowserTestBase::SetUp()
#21 0x00000209ffe2 InProcessBrowserTest::SetUp()
#22 0x0000006885ee testing::Test::Run()
#23 0x000000689110 testing::TestInfo::Run()
#24 0x0000006895f7 testing::TestCase::Run()
#25 0x00000068fa67 testing::internal::UnitTestImpl::RunAllTests()
#26 0x00000068f6f3 testing::UnitTest::Run()
#27 0x000002cceca4 base::TestSuite::Run()
#28 0x00000055b47c InteractiveUITestSuiteRunner::RunTestSuite()
#29 0x0000024d3e7d content::LaunchTests()
#30 0x00000055b3f8 main
#31 0x7f904d54ef45 __libc_start_main
#32 0x00000044bff0 <unknown>

I cannot reproduce the same failure locally though and cannot identify a culprit, any ideas?

Seems like the original issue has recovered itself, but OmniboxViewTest issue
is happening sporadically.

I'm closing this bug and file a new bug for OmniboxViewTest (since this bug is
not very clear about the scope).