To center all elements in the navbar, simply apply the justify-content-center class to the nav element.
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.4.1/js/bootstrap.min.js"></script>
<link href="https://stackpath.bootstrapcdn.com/bootstrap/4.4.1/css/bootstrap.min.css" rel="stylesheet" />
<nav class="navbar navbar-light bg-light justify-content-center">
<a class="navbar-brand" href="#">
<img src="/docs/4.4/assets/brand/bootstrap-solid.svg" width="30" height="30" class="d-inline-block align-top" alt="">Bootstrap</a>
<div class="d-flex">
<form class="form-inline">
<input class="form-control mr-sm-2" type="search" placeholder="Search" aria-label="Search">
<button class="btn btn-outline-success my-2 my-sm-0" type="submit">Search</button>
</form>
</div>
</nav>
If you want to center the search block within the navbar, you can add an empty div at the end of the nav and use the justify-content-between class on the nav element.
Note: This may not be the most elegant solution.
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.4.1/js/bootstrap.min.js"></script>
<link href="https://stackpath.bootstrapcdn.com/bootstrap/4.4.1/css/bootstrap.min.css" rel="stylesheet" />
<nav class="navbar navbar-light bg-light justify-content-between">
<a class="navbar-brand" href="#">
<img src="/docs/4.4/assets/brand/bootstrap-solid.svg" width="30" height="30" class="d-inline-block align-top" alt="">Bootstrap</a>
<div class="d-flex">
<form class="form-inline">
<input class="form-control mr-sm-2" type="search" placeholder="Search" aria-label="Search">
<button class="btn btn-outline-success my-2 my-sm-0" type="submit">Search</button>
</form>
</div>
<div></div>
</nav>