This GreaseMonkey Script will allow use of the FullScreen button for YouTube embeds in Instapaper:

// ==UserScript==
// @name        Instapaper Full Screen Youtube
// @namespace   net.blackpacket.instapaper.fullscreenyoutube
// @description Allow Youtube Embeds in Instapaper to go fullscreen
// @include     instapaper.com
// @version     1
// @grant       none
// ==/UserScript==

var iframes = document.getElementsByTagName("iframe");
for(var i=0;i<iframes.length;i++) {
  iframes[i].setAttribute("allowfullscreen","");
}