PHP does not refresh the page so you can initialize your javascript with the date of the server:
<?php
date_default_timezone_set('America/Sao_Paulo');
?>
<div class="date">BR, <span id="server_time"></span></div>
<script>
var server_time = document.getElementById("server_time");
var now = new Date(<?=date('Y')?>, <?=date('m')-1?>, <?=date('d')?>, <?=date('H')?>, <?=date('i')?>, <?=date('s')?>, 0);
window.setInterval(function(){
now.setSeconds(now.getSeconds() + 1);
server_time.innerHTML = now.getDate() + "/" + (now.getMonth() + 1 )+ "/" + now.getFullYear() + " " + now.getHours() + ":" + now.getMinutes() + ":" + now.getSeconds();
},1000);
</script>
Why I did not put the date inside the new Date (), because what works in chrome does not work firefox, in which case it will always work in both.
You can improve the code to show 0, so it would look like 3:03:03 and not 3: 3: 3.