gorbuz9kin,
или просто взять стиль backgroundImage из самой ссылки
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<title> - jsFiddle demo by gorbuz9kin</title>
<style type='text/css'>
.dropdown-menu ul {
margin: 0;
padding: 0;
width: 135px;
list-style: none;
display: none;
}
.dropdown-menu ul li {
background: #0085b6;
height: 35px;
}
.dropdown-menu ul li:hover {
background: #1d9fcb;
}
.dropdown-menu ul li a {
display: block;
width: 100%;
padding: 5px 35px;
text-decoration: none;
font-size: 15px;
color: #fff;
}
.dropdown-menu ul li:first-child a {
background: url(http://abali.ru/wp-content/uploads/2010/12/united-kingdom-flag-16x16.png) no-repeat 5px center;
}
.dropdown-menu ul li:nth-child(2) a {
background: url(http://abali.ru/wp-content/uploads/2010/12/russia-flag-16x16.png) no-repeat 5px center;
}
.dropdown-menu ul li:last-child a {
background: url(http://abali.ru/wp-content/uploads/2010/12/ukraine-flag-16x16.png) no-repeat 5px center;
}
.dropdown-menu .title {
display: inline-block;
width: 80px;
height: 20px;
padding: 5px 0 5px 35px;
font-size: 15px;
line-height: 20px;
cursor: pointer;
background: #eaecf0 url(http://abali.ru/wp-content/uploads/2010/12/united-kingdom-flag-16x16.png) no-repeat 5px center;
}
.dropdown-menu .title::after {
content: "";
float: right;
display: block;
background: url(img/arrow_down.png) no-repeat 10px center;
width: 20px;
height: 20px;
margin-right: 10px;
}
.dropdown-menu.open .title {
background: #0085b6 url(img/flag_english_active.png) no-repeat 5px center;
color: #fff;
border-bottom: 4px solid #1d9fcb;
}
.dropdown-menu.open .title::after {
background: url(img/arrow_up.png) no-repeat 10px center;
}
.dropdown-menu.open ul {
display: block;
}
</style>
<script>
window.onload=function(){
var menuElem = document.getElementById('dropdown-menu'),
titleElem = menuElem.querySelector('.title');
document.onclick = function(event) {
var target = elem = event.target;
while (target != this) {
if (target == menuElem) {
if(elem.tagName == 'A') {
titleElem.innerHTML = elem.textContent;
titleElem.style.backgroundImage = getComputedStyle(elem, null)['backgroundImage']
}
menuElem.classList.toggle('open')
return;
}
target = target.parentNode;
}
menuElem.classList.remove('open');
}
}
</script>
</head>
<body>
<div id="dropdown-menu" class="dropdown-menu">
<span class="title">English</span>
<ul>
<li><a href="#">English</a></li>
<li><a href="#">Русский</a></li>
<li><a href="#">Украинский</a></li>
</ul>
</div>
</body>
</html>