What I have done below is a simplified method for the iframe waiting to be loaded, and meanwhile in the background a gif is shown. When the iframe is completely loaded, the gif disappears. Be aware that this is specific for jQuery.
I have removed the <img> of your code, this won't work. I have simplified it by adding a class to div#printdiv called load-gif and gave it background styling.
I have also added an opacity function. Otherwise you see a page being loaded in the iframe while the gif is still in the background. To avoid this iframe is invisible (opacity: 0;) until it's fully loaded and then opacity turns back to opacity: 1;.
body {
  height: 40vw;
  width: 100%;
  background-color: #e4e4e4;
}
#printdiv {
  display: flex;
  align-items: center;
  justify-content: center;
  border: 1px solid #e4e4e4;
  height: 100%;
  margin: 3em;
}
#printdiv>p,
body>div,
#frame1 {
  width: 100%;
  height: 100%;
}
#printdiv,
#frame1 {
  background-color: white;
}
/* Below CSS are the important factors, above is just example styling. */
#frame1 {
  opacity: 0; /* set at 0 to avoid gif and iframe mixture in the same div */
}
.load-gif { /* extra class to load gif */
  background: url(https://loading.io/assets/img/ajax.gif) center no-repeat;
  background-size: contain;
}
<!-- begin snippet: js hide: false console: true babel: false -->
<html>
<head>
  <script src="http://code.jquery.com/jquery-latest.js"></script>
  <script>
    jQuery(document).ready(function() { // starts DOM page is ready
      jQuery("#frame1").on("load", function() { // when iframe is completely loaded
        jQuery(".load-gif").css("background", "unset"); // removes gif
        jQuery(this).css("opacity", "1"); // set opacity to normal value
      });
    });
  </script>
</head>
<body>
  <div>
    <div id="printdiv" class="load-gif">
      <p>
        <iframe id="frame1" src="/" frameborder="0"></iframe>
      </p>
    </div>
  </div>
</body>
</html>
 
 
An alternative way is to remove the load-gif class completely after iframe is loaded. jQuery will look like this:
jQuery(document).ready(function() { // starts DOM page is ready
  jQuery("#frame1").on("load", function() { // when iframe is completely loaded
    jQuery('#printdiv').removeClass("load-gif"); // removes gif class
    jQuery(this).css("opacity", "1"); // set opacity to normal value
  });
});