The slider is set to display a custom excerpt of content, and HTML tags have been stripped out to avoid the more common issue of shortcodes or unnecessary HTML being displayed on the excerpt.
While I can't vouch for how this will affect excerpts elsewhere on your slides, you can change this by going into the recent-posts-flexslider.php file in the plugin directory, and edit line 230, near the bottom of the file.
// Remove tags from excerpt
$string = strip_tags( $string );
Just delete those lines entirely (or comment line 230 with // like the line above) and your links will display.
Thanks for trying the plugin!