input-group-addon within input-group is not flipped!

[MikeAlhayek]

Here is the Html code that I am using

<div class="form-group">
    <label for="pick_up_time" class="col-md-2 control-label">Some Label</label>
    <div class="col-md-10">
        <div class="input-group input-width-input time-picker">
            <input class="form-control" name="pick_up_time" type="text" id="pick_up_time" value="" required>
            <span class="input-group-addon">
                <span class="glyphicon glyphicon-time"></span>
            </span>
        </div>
    </div>
</div>

This is how it looks when using using bootstrap-flipped.min.css file