With string concatenation, your also need to include the variables file before assigning them variables to the array. You also dont need to wrap PHP variables in quotes when echoing.
<?php include('includes/variables.php'); ?>
<ul data-options="[orbit options go here]" data-orbit>
<?php
$links = array(
'<li data-orbit-slide="headline-1"><img /><div>'.$Slide1.'</div></li>',
'<li data-orbit-slide="headline-2"><img /><div>'.$Slide2.'</div></li>',
'<li data-orbit-slide="headline-3"><img /><div>'.$Slide3.'</div></li>',
);
shuffle($links);
foreach ($links as $link) { echo $link; } //<<< notice no quotes
?>
</ul>
Edit:
Can I make a suggestion to your code, by assigning to a slides array directly be it in an external file or not, you will be able to eventually dynamically or easily add new slides to the slider and not need to hard code into a second sub array before the loop. So something like. Also by changing to alternative syntax your keep a nice HTML structure.
<?php
$slide[] = "<h5>Slide 1</h5><h6>This is the content for slide 1!</h6>";
$slide[] = "<h5>Slide 2</h5><h6>This is the content for slide 2!</h6>";
$slide[] = "<h5>Slide 3</h5><h6>This is the content for slide 3!</h6>";
shuffle($slide);
?>
<ul data-options="animation:fade; slide_number:false; pause_on_hover:false; timer_speed:5500; navigation_arrows:false; next_on_click:true; timer:true; bullets:false;" data-orbit>
<?php foreach ($slide as $key=>$value):?>
<li data-orbit-slide="headline-<?php echo $key?>"><img /><div><?php echo $value; ?></div></li>
<?php endforeach;?>
</ul>