Show taxonomy list with taxonomy images ( SOLVED)

Unfortunately, it looks like the code that runs your widget will not let you add your image: The code here shows that a loop is creating the unordered list and there are no filters where you can inject your own image.

You can add your own code to the plugin, but it’s not recommended as once you push an update it will break. You may also be able to add some custom CSS that adds background images to a custom element inside the list tag. I created this quick example that may help.

.ve-cat-widget-listing li:before{
    content:'';
    display:block;
    width:140px;
    height:100px;
    outline:1px solid red;
    background-image:url(https://via.placeholder.com/140x100); /*Will need to add dynamic image from ACF */
    background-repeat:no-repeat;
    background-position:center center;
}

EDIT
From my comment below, if you would rather edit the plugin directly you could add the ACF image field like this:

if ( $tax_img = get_field('YOUR_ACF_ID_HERE', $term->term_id)) {
    $va_category_HTML .= sprintf('<img src="https://wordpress.stackexchange.com/questions/338877/%s" />', $tax_img);
}