Just create a new 'polylang' subdirectory in 'wp-content/', then put your flag es_ES.png or es_ES.jpg (provided that you use es_ES as locale) in this directory wp-content/polylang/. The flag will be modified on frontend only, not on admin side.
Your link works today. I guess you want to put your flags in place of the phone on top right. I suppose that this phone number is not present in the distributed theme. In that case, you should find something like (maybe in header.php):
Just after this, write:
<ul class="lang-switch"><?php pll_the_languages(array('show_flags'=>1,'show_names'=>0));?></ul>
Then add the following lines in style.css:
Maybe, you will obtain what you want...
And of course, you should do this in child theme otherwise you will loose your modifications at the next theme update.