Just in case, if someone needs to use typeahead with a Kentico .json file:
using a file like:
{myKenticoSite}/rest/cms.country?format=json&columns=CountryName
(be aware... json can be case sensitive...)
<script type='text/javascript'> 
$(window).load(function(){
    var v01 = new Bloodhound({
        limit: 10,
        datumTokenizer: function (d) {
            return Bloodhound.tokenizers.whitespace(d.value);
        },
        queryTokenizer: Bloodhound.tokenizers.whitespace,
        prefetch: { 
            url: '{myKenticoSite}/rest/cms.country?format=json&columns=Countrydisplayname',
            filter: function (v01) {  
                return $.map(v01.cms_countries[0].cms_country, function (myCountry) {  
                    return {        
                        value: myCountry.Countrydisplayname 
                    };
                });
            }
        }
    });
    // Initialize the Bloodhound suggestion engine
    v01.initialize(); 
    // Instantiate the Typeahead UI
    $('.typeahead').typeahead(
        {
            hint: true,
            highlight: true,
            minLength: 1
        }, 
        {
        //displayKey: 'value',
        displayKey: function (f01) {
                  return f01.value;
              },
        source: v01.ttAdapter()
    });
}); 
</script> 
<div class="bs-example">
        <input class="typeahead">
</div>