Prevent a flex items height from expanding to match other flex items

This is an old solution. My answer is superseded by this new answer by Aaron using align-self. That is a better solution that does not rely on a CSS quirk.

As long as the flex container has no height itself, you can set height: 0% on the first flex item. Because it has no height to inherit from its parent, any percentage height will cause it to collapse. It will then grow with its contents.

Example

In this example I have removed the -webkit prefix. It's only really required for Safari and the prefix can be added above the non-prefixed version. I also removed flex-direction: row as it is the default value.

.container {
  display: flex;
}
.flexbox-1 {
  flex: 1;  
  height: 0%;  
  border: solid 3px red;
}
.flexbox-2 {
  flex: 2;
  border: solid 3px blue;
  height: 200px;
  margin-left: 10px;
}

<div class="container">
  <div class="flexbox-1">.flexbox-1</div>
  <div class="flexbox-2">.flexbox-2</div>
</div>

I know this is an old question but a better solution is to set the flex item to align to the top using flex-start.

/* Default Styles */
.container {
  display: flex;
}
.flexbox-2 {
  flex: 2;
  border: solid 3px blue;
  height: 200px;
  margin-left: 10px;
}
 .flexbox-1 {
  flex: 1;  
  align-self: flex-start;  
  border: solid 3px red;
}

<div class="container">
  <div class="flexbox-1">"align-self: flex-start;"</div>
  <div class="flexbox-2">.flexbox-2</div>
</div>