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>