JSFiddle - React, Tailwind, and code Playground

HTML

<div class="person">
    <div class="controls controls-row">
      <input class="span3" placeholder="First Name" type="text" name="firstname1">
      <input class="span3" placeholder="Last Name" type="text" name="lastname1">     
         <select class="span2" name="gender1"><option value="Male">Male</option><option           value="Female">Female</option></select>   
    </div>
</div>

<a href="#" id="addRow"><i class="icon-plus-sign icon-white"></i> Add another family member</p></a>

JavaScript

$(document).ready(function(){
        $('#addRow').click(function(){
            // get the last person and html html
            var $person = $('.person').last();
            var person = $person.html();
            // find the number
            var index = person.indexOf('firstname');
            var number = parseInt(person.substring(index+9,1));
            var next = number+1;
            // replace the number
            // for firstname
            person.replace('firstname'+number, 'firstname'+next);
            // for lastname
            person.replace('lastname'+number, 'lastname'+next);
            // for gender
            person.replace('gender'+number, 'gender'+next);
            // insert the new person after the last one
            $person.after($('<div class="person">'+person+'</div>'));            
            // get the new person
            var $new = $('.person').last();
            // hide it
            $new.hide();
            // reset the values
            $new.find('input, select').val('');
            // fade it in
            $new.slideDown();
         });
    })