In order to get a search box for your website that uses DuckDuckGo, you can use the following snippet.

<form target="_blank" method="get" action="https://duckduckgo.com">
    <!-- Search box -->
    <input name="q" type="text" placeholder="Search terms" />

    <!-- The website to search -->
    <input value="gkbrk.com" name="sites" type="hidden" />

    <!-- Region for localization, optional -->
    <input value="uk-en" name="kl" type="hidden" />
</form>