полагаю как то так
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Document</title>
<style>
.block{
display: none;
}
</style>
</head>
<body>
<button>Пуск</button>
<div class="block">1</div>
<div class="block">2</div>
<div class="block">3</div>
<div class="block">4</div>
<div class="block">5</div>
<div class="block">6</div>
<div class="block">7</div>
<div class="block">8</div>
<div class="block">9</div>
<div class="block">10</div>
<script>
document.querySelector('button').onclick = function(){
var block = [...document.querySelectorAll('.block')].sort(_=>Math.random() - 0.5), i = 0;
(run=()=>{
block[i].style.display = 'block';
setTimeout(()=>{
block[i].style.display = 'none';
if(++i<block.length) run();
},1000); //время
})();
};
</script>
</body>
</html>