I know its quite late to answer this, but I guess it will help anyone ahead.
Well using CSS3 FlexBox. It can be acheived.
Make you header as display:flex
and divide its entire width into 3 parts. In the first part I have placed the logo, the searchbar in second part and buttons container in last part.
apply justify-content: between
to the header container and flex-grow:1
to the searchbar.
That's it. The sample code is below.
#header {_x000D_
background-color: #323C3E;_x000D_
justify-content: space-between;_x000D_
display: flex;_x000D_
}_x000D_
_x000D_
#searchBar, img{_x000D_
align-self: center;_x000D_
}_x000D_
_x000D_
#searchBar{_x000D_
flex-grow:1;_x000D_
background-color: orange;_x000D_
padding: 10px;_x000D_
}_x000D_
_x000D_
#searchBar input {_x000D_
width: 100%;_x000D_
}_x000D_
_x000D_
.button {_x000D_
padding: 22px;_x000D_
}_x000D_
_x000D_
.buttonsHolder{_x000D_
display:flex;_x000D_
}
_x000D_
<div id="header" class="d-flex justify-content-between">_x000D_
<img src="img/logo.png" />_x000D_
<div id="searchBar">_x000D_
<input type="text" />_x000D_
</div>_x000D_
<div class="buttonsHolder">_x000D_
<div class="button orange inline" id="myAccount">_x000D_
My Account_x000D_
</div>_x000D_
<div class="button red inline" id="basket">_x000D_
Basket (2)_x000D_
</div>_x000D_
</div>_x000D_
</div>
_x000D_