How do I make multiple dependent input fields that use the jquery autocomplete function?

Add a autocomplete ‘select’ catch to your first autocomplete field. Use this to get the chosen value from the autocomplete. Use an Ajax call to obtain your next autocomplete source based on the selected value and apply the new source to the next autocomplete field.

jQuery( "#cns-make" ).autocomplete({
    source: availableTags,
    select: function (event, ui) {
        var data = new FormData();
        var value = ui.item.value;
        data.append( 'action', 'your_function' );
        data.append( 'varname', value );
        jQuery.ajax({
            url: ajax_url,
            type: 'POST',
            data: data,
            success: function( response ) { // response is a json string returned from your_function
                jQuery( "#cns-category" ).autocomplete( 'option', 'source', response );
            }
        })
    }
});

Reference