Google Chrome bookmarks export
perhaps you have tried achieving this with syncing your bookmarks over google account? I am aware that stock browser checks out the bookmarks synced with google account when logged in. If you log into google using chrome browser, syncing bookmarks and then logging into google utilizing stock web browser should ensure you get your bookmarks here. Cannot test it because I am at this time on 4.2.2 and do not have Chrome for android put in so this is just a guess how it might be done.
When you first start your chrome browser it requires you right-away to login to your google account. For those who have done so it asks you the same question as with the desktop variation - whether or not to synchronize things like passwords, bookmarks etc. between chrome instances. When you have done the very first thing and answered these question with "yes every thing" or simply "yes" with a marked checkbox for bookmarks you are pretty much put up. If you don't have this done yet you can easily reconfigure synchronisation in chrome configurations.
Now if you take a research the bookmarks element of chrome you really need to see some folders like "mobile bookmarks", "other bookmarks", "desktop bookmarks" (due to my german variation the titles may vary a little). Every bookmark saved under "desktop bookmarks" would be synchronized back again to your google account. If you open your stock android browser some mins later on and login to your google account when requested you will notice your yahoo email as a folder/category inside bookmarks section containing your bookmarks from chrome. Even if you will install in other words. a chrome internet browser on your desktop some time you will be together with your bookmarks/tabs/passwords/... beeing pulled from your own google account when you login.