Thank you for contacting WPML Support. I’ve visited your site and found out that there was a CSS conflict that’s why you are facing these issues and could be fixed easily by adding this small CSS:
.wpml-ls-menu-item .wpml-ls-flag {
width: auto !important;
}
.wpml-ls-item a {
display: inline-block !important;
}
In the custom CSS section of your theme and it will look as in the attached screenshot.
Could you please give it a try and let me know how it goes?