I just tested the plugin on a brand new WordPress install (version 5.0.3 just like yours) with the Twenty Seventeen theme activated and the plugin is working OK with its default settings. A few things you can check:
First, the snowflakes may be hard to see if you have a white background. Try changing their color to see if they are there. Also check if any of the advanced settings have been changed that may affect the positioning of the flakes.
View the source of the home page. Near the bottom in the HTML you should see some JavaScript output from the plugin like this:
<script type='text/javascript'>
/* <![CDATA[ */
var flurryOptions = {"container":"body"};
/* ]]> */
</script>
<script type='text/javascript' src='https://diskstation918.localdomain:8080/wp-content/plugins/flurry/public/js/jquery.flurry.min.js?ver=1.1.0'></script>
<script type='text/javascript'>
jQuery( document ).ready( function( $ ) {
// Cast boolean options as boolean if necessary
if ( flurryOptions.blur ) {
flurryOptions.blur = flurryOptions.blur === "true";
}
$( flurryOptions.container ).flurry( flurryOptions );
});
</script>
If you don’t see that output, something else may be preventing the plugin from working properly.
Also check for any errors in your browser dev tools console. That’s usually F12 on Windows or Cmd+Option+I on macOS.