JSFiddle - React, Tailwind, and code Playground

HTML

<p>flex-basis: 100% - correct (as stated in my answer)</p>
<div class="header">
  <div class="item flex-basis">asdfasdfasdfasdfasdfasdf</div>
  <div class="item flex-basis">z</div>
</div>

<p>flex: 1 - correct (as stated in my answer)</p>
<div class="header">
  <div class="item flex-shorthand">asdfasdfasdfasdfasdfasdf</div>
  <div class="item flex-shorthand">z</div>
</div>

<p>flex: 1 1 0 - correct (as stated in my answer)</p>
<div class="header">
  <div class="item flex-long">asdfasdfasdfasdfasdfasdf</div>
  <div class="item flex-long">z</div>
</div>

<p>flex: 1 1 auto - incorrect (as stated by your comment)</p>
<div class="header">
  <div class="item flex-long-auto">asdfasdfasdfasdfasdfasdf</div>
  <div class="item flex-long-auto">z</div>
</div>

CSS

.header {
  display: flex;
}

.item {
  text-align: center;
  border: 1px solid black;
}

.flex-basis {
  flex-basis: 100%;
}

.flex-shorthand {
  flex: 1;
}

.flex-long {
  flex: 1 1 0;
}

.flex-long-auto {
  flex: 1 1 auto;
}