For full screen to work you need player interaction. I've changed the generated index.html to accomodate:
Replace the body script with something like this:
<body style='cursor: pointer' onclick="document.body.removeChild(document.getElementById('click'));
if(document.getElementById('openfl-content').name===undefined){ document.getElementById('openfl-content').name='openfl-content';if (
document.fullscreenElement ||
document.webkitFullscreenElement ||
document.mozFullScreenElement ||
document.msFullscreenElement || document.webkitEnterFullscreen
) {
if (document.exitFullscreen) {
document.exitFullscreen();
} else if (document.mozCancelFullScreen) {
document.mozCancelFullScreen();
} else if (document.webkitExitFullscreen) {
document.webkitExitFullscreen();
} else if (document.msExitFullscreen) {
document.msExitFullscreen();
}
} else {
element = document.documentElement;
if (element.webkitEnterFullScreen){
element.webkitEnterFullScreen();
} else if (element.requestFullscreen) {
element.requestFullscreen();
} else if (element.mozRequestFullScreen) {
element.mozRequestFullScreen();
} else if (element.webkitRequestFullScreen) {
element.webkitRequestFullScreen();
} else if (element.webkitRequestFullscreen) {
element.webkitRequestFullscreen();
} else if (element.msRequestFullscreen) {
element.msRequestFullscreen();
}
} lime.embed ('YourGameName', 'openfl-content', 1280, 640, { parameters: {} }); }" >
<div id="openfl-content" ></div>
<div id='click' style='position:absolute; top:256px; left:256px; color:blue;'> <H1 > CLICK TO START </H1> </div>
</body>
</html>