Basic animates can't animate non-numeric CSS properties.
so use step function in animate then it works.
See example: http://jsfiddle.net/kevalbhatt18/epp06LL3/2/
 $('#box').animate({  transformValue: -180 }, {
    step: function(now,fx) {
      $(this).css('transform','rotatex('+now+'deg)');  
    },
    duration:'slow'
},'linear');
EDIT:
See example: http://jsfiddle.net/kevalbhatt18/u2ptr4jp/4/
Now simply add div inside parent span it will work for all.
Note: only first class you should know i.e in this example we have
  box class so if we are at last box then it will flip to first box
$("div").click(function() {
    var that = this;
    $(this).animate({
        transformValue: -180
    }, {
        step: function(now, fx) {
            $(this).css('transform', 'rotatey(' + now + 'deg)');
        },
        complete: function() {
            $(that).hide();
            //$('#box').removeAttr( 'style' );
            var nextObject = $(that).next()
             var nextClass = nextObject.attr('class')
            console.log($('#parent').children().hasClass(nextClass));
            if ($('#parent').children().hasClass(nextClass)) {
                var flipNext = nextClass;
                console.log("true")
            } else {
                console.log("false")
                var flipNext = "box";
                console.log(flipNext);
            }
            secondFlip(flipNext, that);
        },
        duration: 'slow'
    }, 'linear');
});
function secondFlip(nextID, that) {
    $('.' + nextID).show();
    $('.' + nextID).animate({
        transformValue: 180
    }, {
        step: function(now, fx) {
            $(this).css('transform', 'rotatex(' + now + 'deg)');
        },
        complete: function() {
        },
        duration: 'slow'
    }, 'linear');
}
Edit: rotation issue solved
see this example: http://jsfiddle.net/kevalbhatt18/u2ptr4jp/6/
Final Output:
After so many tray I found solution.
see this example:http://jsfiddle.net/kevalbhatt18/oh07zuh0/
hear i find transformation degree.
(function ($) {
    $.fn.rotationDegrees = function () {
        var matrix = this.css("-webkit-transform") || this.css("-moz-transform") || this.css("-ms-transform") || this.css("-o-transform") || this.css("transform");
        if (typeof matrix === 'string' && matrix !== 'none') {
            var values = matrix.split('(')[1].split(')')[0].split(',');
            var a = values[0];
            var b = values[1];
            var angle = Math.round(Math.atan2(b, a) * (180 / Math.PI));
        } else {
            var angle = 0;
        }
        return angle;
    };
}(jQuery));