Replace following code in header.php:
<h1 id='logo'><a href="<?php echo get_settings('home'); ?>/"><?php bloginfo('name'); ?></a></h1>
with:
<h1 id='logo'><a href="<?php echo get_settings('home'); ?>/"><?php bloginfo('name'); ?></a></h1>
<div class="flags">
<a href="link-to-my-other-website.com"><img src="my-flag" alt="language" /></a>
<a href="link-to-my-other-website.com"><img src="my-flag" alt="language" /></a>
</div>
Then add following code to style.css:
.flags{
position: absolute;
top: 40px;
right: 0px;
z-index:20;
}
Adjust the top and right value as you like (you can position the flags anywhere you like - just play around with the pixel values).