How to add Emoji tab in Chrome touch bar?
How add emoji tab in customised touch bar in Macbook Chrome browser?
MacBook Pro TouchBar and Touch ID, iOS 11.2.5
Unfortunately the Chrome browser does not support the emoji menu in the TouchBar. For general information on the Touch Bar, check out this support article. Sorry I couldn't provide a more helpful solution, but Apple does limit the customizability of the Touch Bar. Other apps are available for the Touch Bar from third parties (not all are in the Mac App Store) which could potentially offer some resolution for your problem.