Unfortunately, Flash games are dying and Internet browsers don't thoroughly support them any more. Still we can play them but we should give a permanent permission to Adobe Flash Player. First you have to install Adobe Flash Player if you don't have it: Click here to get it from Adobe's official site: https://get.adobe.com/flashplayer/
Then you must allow Flash content in Chrome by choosing "always" option. All of these take just a few minute. After installation and giving the required permision for once, restart Chrome and wait for a while. UNO will be loading very slowly but this is just for once, too. Then you'll never have any problem.
Watch the short video here to learn how to allow Flash content on Chrome browser permanently:
Have fun & best wishes,