When used in an <image> tag SVG must be contained in a single file for privacy reasons. This bugzilla bug has more details on exactly why this is so. Unfortunately you can't use a different tag such as an <iframe> because that won't work as a link so you'll have to embed the CSS in a <style> tag within the file itself.

When used in an <image> tag SVG must be contained in a single file for privacy reasons. This bugzilla bug has more details on exactly why this is so. Unfortunately you can't use a different tag such as an <iframe> because that won't work as a link so you'll have to embed the CSS in a <style> tag within the file itself.

One other way to do this would be to have the SVG data within the main html file i.e.

<a href='http://youtube.com/...' target='_blank'>
  <svg id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 56.69 56.69">
    <g>
        <path d="M28.44......./>
    </g>
  </svg>
</a>

You could style that with an external CSS file using the HTML <link> tag.