In your modal, put an id for the iframe, so it'll be:
<iframe id="video-frame" src=""></iframe>
In your link, create a custom attribute, let's say video-src, so it'll be:
<a class="show-vid-modal" href="#" video-src="<?php echo $v_vid['vid_link']; ?>"><?php echo $v_vid['vid_title'] ?></a>
Once you have it, put in your button's click function:
$('.show-vid-modal').click(function(e) {
//here the attribute video-src is helpfull
var vid-src = $(this).attr('video-src');
var title = $(this).html();
e.preventDefault();
$("#vid-modal").on('show.bs.modal', function(e) {
$("h4 #modal-title").text(title);
//here the id for the iframe is helpfull
$('#video-frame').attr('src', vid-src);
});
$("#vid-modal").modal();
});
It might work.