It's even simpler than using an extension: the History page in Chrome is already an HTML page, as are all the other panes and pages in Chrome. This may be more than a year late to this question, but You can use Google Takeout to download a json file of your Android Chrome history. You can also. Using this tool is very simple, you just need to download the 180KB ZIP file and run it from any folder. The utility reads the Google Chrome Web.
How to download chrome history to a file - for that
How to download chrome history to a file - not absolutely
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