div{
  display:flex;
  border:1px solid red;
}
div button{
  flex:0 0 1;
  border:1px solid gray;
}<div>
   <button>Button one</button>
   <button>Button two</button>
</div>div{
  display:flex;
  border:1px solid red;
}
div button{
  flex:0 0 1;
  border:1px solid gray;
}<div>
   <button>Button one</button>
   <button>Button two</button>
</div> 
    
     
    
    Try this
div{
  display:flex;
  border:1px solid red;
}
div button{
  flex: 1;
  border:1px solid gray;
}<div>
   <button>Button one</button>
   <button>Button two</button>
</div> 
    
    First, you have a typo "dispaly:flex;". :) 
Second, just put flex-grow: 1; on the buttons. 
Example code:
div{
  display:flex;
  border:1px solid red;
}
div button{
  flex-grow: 1;
  border:1px solid gray;
}
Hope it helps.
Should be this.
div {
  display: flex;
  border: 1px solid red;
}
div button {
  flex: 0 0 50%;
  border: 1px solid gray;
}<div>
   <button>Button one</button>
   <button>Button two</button>
</div>