You can get bookmarks and history dumps with the following shell commands:
adb shell content query --uri content://com.android.chrome.browser/bookmarks
adb shell content query --uri content://com.android.chrome.browser/history
I got the following error after running this command:
…
Permission Denial: opening provider com.google.android.apps.chrome.ChromeBrowserProvider
…
Do you have any ideas how to get the permission? I think the commands are only working on rooted devices.
With Browser History you can also search and backup your Browser History.