I try the following sketch (https://jsfiddle.net/m4njf8bL/):
<div style="position: relative; display: flex; height: 100px; border: 1px solid red; padding: 5px;">
<button style="position: relative; display: flex; flex: 1 1 auto; flex-direction: column; align-items: stretch; justify-content: center; border: 1px solid green; ">
<span style="display: flex; flex: 1 1 auto; align-items: stretch; justify-content: center; border: 1px solid blue;">Ololo</span>
</button>
</div>
The inner span stretches vertically in all browsers except for Firefox. Why and is there a workaround?