How do I keep Chrome bookmarks in sync across accounts?

No direct way, but you can copy Folders from Bookmark Managers of different accounts

1. Go to top right corner of Crome
2. Click Manage People
3. Add Person - This is where you will add another Crome Account
4. Now go to Bookmark Manager right click on any subfolder from Bookmarks Bars or Other Bookmarks, select copy (You can even directly copy folders from bookmark bar)
5. Now open new Crome window and login with other user
6. Open Bookmark Manager from this new window and right click to paste your copied bookmark folder.

There isn't a simple way to keep the bookmarks in sync between accounts. However, it is possible to log in with multiple Google Account, albeit not on the Global/Browser/Profile level (which is what you are doing now).

In order to log in with multiple Google accounts, go to any Google site, such as accounts.google.com. There, you will be able to log in with multiple accounts (usually, there is something like "Add Account" or "Manage Accounts", depending on which Google site you go to).

Once you have logged in with multiple accounts, you will be able to easily switch between your accounts when you go to YouTube, check email, etc. Note that you are still signed in as a single Profile in terms of the Bookmarks, etc. As such, you will always be able to access your bookmarks and such regardless of which account you are viewing on the sites themselves.

For most (if not all) of Google sites, you can switch profile by clicking on your Profile Picture. As a matter of fact, that is also where you can add new accounts.

In case if you want to merge the bookmarks from two different accounts, open chrome with those two different accounts, open bookmark manager of both profiles, copy the bookmarks folder/file from one profile and paste it into another profile. Way to go!