How do I iterate through this JSON object in jQuery?

Since you tagged your question as a jquery one, you should use $.each because it’s jquery’s iterator function:

$.each(data.dates, function(index, element) {
    alert(element.timeStamp); 
});

If you want to stick to the for in syntax (which i see you’ve tried), a solution might be :

for(var key in data.dates) {
     alert(data.dates[key].timeStamp); 
} 

But beware that the for in syntax may do more than you think it does: it iterates over the properties inherited from the prototype too, so it might be usefull to make sure you iterate only on the object instance properties:

for(var key in data.dates) {
    // if it's not something from the prototype
    if(data.dates.hasOwnProperty(key)) {
        alert(data.dates[key].timeStamp); 
    }
} 

update
Another elegant way is to use the Object.keys method that returns an array containing all the keys in the targeted object to iterate over all the object’s properties:

for(var i=0, keys=Object.keys(data.dates), l=keys.length; i<l; i++) {
    alert(data.dates[i].timeStamp);
}