<iframe src="https://cdn.rawgit.com/Triforcey/clip-j/38e8bf144e4633fffde57c675171b22211174e24/test.html" frameborder="0" width="100%" height="100%" style="margin: 0px;"></iframe>
This is possible, despite the many people who do not know about this solution. (It's very new.) I have created an extremely easy to use JavaScript library for this called clip-j. Here is the GitHub page. Basically how it works is it takes advantage of document.execCommand('copy');
with a few other lines of code to optimize it to get around the limitation that you need to be able to see the copied text. So this simple solution requires on no Flash, and is completely invisible! Here is the source code:
function clip(text) {
var copyElement = document.createElement('input');
copyElement.setAttribute('type', 'text');
copyElement.setAttribute('value', text);
copyElement = document.body.appendChild(copyElement);
copyElement.select();
document.execCommand('copy');
copyElement.remove();
}