How can I reorder my divs using only CSS?

A CSS-only solution (works for IE10+) – use Flexbox’s order property:

#flex { display: flex; flex-direction: column; }
#a { order: 2; }
#b { order: 1; }
#c { order: 3; }

<div id="flex">
   <div id="a">A</div>
   <div id="b">B</div>
   <div id="c">C</div>
</div>