Steps to reproduce the problem:
1.  Using Android support lib 27.0.2 setup a Chrome CustomTabsIntent with flags Intent.FLAG_ACTIVITY_NO_HISTORY | Intent.FLAG_ACTIVITY_EXCLUDE_FROM_RECENTS
2. Launch it as a Trusted Web Activity: TrustedWebUtils.launchAsTrustedWebActivity(activity, customTabsIntent, Uri.parse(url));

3. The flags are passed onto IntentDispatcher but not onto WebappActivity. This means the WebappActivity hangs around in the activity stack and recent apps view. Normal custom tabs don't do this as they get the flags passed onto them. 

What is the expected behavior?
Flags passed onto WebappActivity

What went wrong?
Flags were not passed onto WebappActivity

Did this work before? N/A 

Does this work in other browsers? N/A

Chrome version: 65.0.3315.0  Channel: canary
OS Version: 8.1.0
Flash Version: N/A

The above code results in the following logcat:
ActivityManager: START u0 {act=android.intent.action.VIEW dat=<redacted> flg=0x40800000 pkg=com.chrome.canary cmp=com.chrome.canary/com.google.android.apps.chrome.IntentDispatcher (edited)

ActivityManager: START u0 {act=android.intent.action.VIEW dat=<redacted> flg=0x14080000 cmp=com.chrome.canary/org.chromium.chrome.browser.webapps.WebappActivity (has extras)} from uid 10247

The IntentDispatcher is launched with the flags as in the above code (0x40800000) but the WebappActivity is launched with the flags 0x14080000:
FLAG_RECEIVER_FOREGROUND | FLAG_RECEIVER_REGISTERED_ONLY_BEFORE_BOOT | FLAG_ACTIVITY_CLEAR_WHEN_TASK_RESET