It looks like you are adding this element dynamically, so you need to use a delegated event listener:
$(document).on('click', '.request', function() { alert("hi"); });
Also you have a problem with your escaped quotes that don't match. I do not think this is necessary:
<div class="ui-block-c"><a class="request" data-role="button" data-id="'+json[i].num+'" data-type="3" data-icon="plus" data-iconpos="right">Test</a></div>
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