This is the updated code:
<?php
$rows = get_field('slider_image' );
$sub_field = has_sub_field('slider_image');
$rand_row = $rows[ array_rand( $rows ) ];
$logo_colour = get_sub_field('logo_colour');
$caption = get_sub_field('the_caption');
$template_directory = bloginfo('template_directory');
if($rows) // if slider_image exits
{
echo '<h3>Header</h3>';
echo '<ul>';
while($sub_field) // enables us to use get_sub_field
{
$rows = $rand_row['slider_image']; // random order of rows
foreach ($rows as $row) {
echo '<li>' . $caption . '</li>'; // displays caption
if(($logo_colour) == "white") { // displays white logo if selected, else grey
echo '<li><img src="'. $template_directory . '/logo_white.png" /></li>';
} else {
echo '<li><img src="'. $template_directory . '/logo_grey.png" /></li>';
}
}
echo '</ul>';
}
}
?>
