JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="//cdn.datatables.net/1.10.2/css/jquery.dataTables.min.css">
<script src="//cdn.datatables.net/1.10.2/js/jquery.dataTables.min.js"></script>
<table class="table" id="image_table">
    <thead>
        <tr>
            <th>Modo</th>
            <th>Acción</th>
        </tr>
    </thead>
    <tbody></tbody>
</table>
<br>
<button id="newrow">Add new row</button>

JavaScript

// Table config
jQuery('#image_table').dataTable({
    bSort: false,
    bFilter: false, 
    bInfo: false,
    bPaginate: false
});

$('#newrow').click(function() {
    $('#image_table').dataTable().fnAddData
        (
                [
                    '<div id="rb1" class="rdio rdio-default">' +
                        '<input type="radio" name="rotateMode" id="radioDefault1" value="1" checked="checked" />' +
                        '<label for="radioDefault">Paisaje</label>' +
                    '</div>' + 
                    '<div id="rb2" class="rdio rdio-default">' +
                        '<input type="radio" name="rotateMode" id="radioDefault2" value="2" />' +
                        '<label for="radioDefault2">Retrato</label>' +
                    '</div>',
                    '<button onclick="allowImage(this);" class="btn btn-default btn-xs">Allow Image</button>'
                ]
        );

});

allowImage = function(a) {
    var index = $(a).parent().parent().index();
    var row = $('#image_table').dataTable().fnGetData(index);
    var opt = $(row[0]).find('input[name=rotateMode]:radio:checked').val();
    
    alert(opt);
}