When scrolling down the .parent div you should see its red background at the bottom due to the padding-bottom. This works in Chrome, but not in Safari and Firefox.
.container {
  display: flex;
  width: 200px;
  height: 500px;
}
.parent {
  display: flex;
  flex-direction: column;
  background: red;
  padding-top: 20px;
  padding-bottom: 20px;
  overflow: auto;
  flex: 1;
}
.child {
  flex: 1 0 100px;
  background: green;
  border: 1px solid blue;
}<div class="container">
 <div class="parent">
  <div class="child">
   child
  </div>
  <div class="child">
   child
  </div>
  <div class="child">
   child
  </div>
  <div class="child">
   child
  </div>
  <div class="child">
   child
  </div>
  <div class="child">
   child
  </div>
  <div class="child">
   child
  </div>
 </div>
</div>codepen: http://codepen.io/anon/pen/NpvJPY
Edit: This question is different from the proposed duplicate because it regards a problem with a fixed padding in pixels, as opposed to the percentage padding in the duplicate.
 
     
    